Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model

DOI10.1016/j.physd.2019.01.004zbMath1451.35074arXiv1704.01554OpenAlexW2963870770WikidataQ128475958 ScholiaQ128475958MaRDI QIDQ2217909

Jeremy L. Marzuola, Jian-Guo Liu, Dionisios Margetis, Jian-feng Lu

Publication date: 12 January 2021

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.01554

zbMATH Keywords

facetcrystal surfaceBurton-Cabrera-Frank (BCF) modelepitaxial relaxationdegenerate-parabolic PDEsubgradient formalism

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Degenerate parabolic equations (35K65) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Simulation of dynamical systems (37M05) Qualitative investigation and simulation of ordinary differential equation models (34C60)

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Cites Work

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• Scale-invariant extinction time estimates for some singular diffusion equations
• Very singular diffusion equations: second and fourth order problems
• The evolution of a crystal surface: analysis of a one-dimensional step train connecting two facets in the ADL regime
• A continuum description of the energetics and evolution of stepped surfaces in strained nanostructures
• Equations with singular diffusivity
• Motion by mean curvature from the Ginzburg-Landau \(\nabla\phi\) interface model
• Parabolic quasilinear equations minimizing linear growth functionals
• A micromechanical model of surface steps
• Existence Theorems for a Multidimensional Crystal Surface Model
• Numerical Analysis of a Steepest-Descent PDE Model for Surface Relaxation below the Roughening Temperature
• Regularity in Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces
• Derivation of a Continuum Model for the Long-Range Elastic Interaction on Stepped Epitaxial Surfaces in $2+1$ Dimensions
• The Variational Formulation of the Fokker--Planck Equation
• Thin Film Materials
• Continuum Relaxation of Interacting Steps on Crystal Surfaces in $2+1$ Dimensions
• The growth of crystals and the equilibrium structure of their surfaces