Slope selection in unstable multilayer growth in 
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 dimensions: Step flow models with downward funneling

Johnson, I. B.; Rätsch, Christian; Gibou, Frédéric; Margetis, Dionisios

doi:10.1103/physreve.100.052802

Cited by 2 publications

(2 citation statements)

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“…Eq. (24). Subsequently, we scale all length scales and spatial coordinates of our system by this R 0 ; alternatively, set R 0 = 1 = L throughout.…”

Section: A On the Numerical Validation Of Our Approximationsmentioning

confidence: 99%

“…A widely known theory of step motion is the Burton-Cabrera-Frank (BCF) model [15]; see also the earlier works by Kossel and Stranski [16,17] and an important extension by Chernov [18]. The BCF model has been successfully applied to many epitaxial phenomena [4,19], including relaxation and coarsening [20][21][22][23][24], bunching instabilities [3,[25][26][27], stochastic nanoscale fluctuations [3,[28][29][30][31][32][33] and evolution of crystal facets [22,[34][35][36][37]. By the BCF theory, each step moves by exchanging atoms with its environment as adsorbed atoms (adatoms) diffuse on the adjacent terraces.…”

Section: Introductionmentioning

confidence: 99%

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Emergence of local geometric laws of step flow in homoepitaxial growth

Johnson,

Margetis

2022

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Below the roughening transition, crystal surfaces exhibit nanoscale line defects, steps, that move by exchanging atoms with their environment. In homoepitaxy, we analytically show how the motion of a step train in vacuum under strong desorption can be approximately described by nonlinear laws that depend on local geometric features such as the curvature of each step, as well as suitably defined effective terrace widths. We assume that each step edge, a free boundary, can be represented by a smooth curve in a fixed reference plane for sufficiently long times. Besides surface diffusion and evaporation, the processes under consideration include kinetic step-step interactions in slowly varying geometries, material deposition on the surface from above, attachment and detachment of atoms at steps, step edge diffusion, and step permeability. Our methodology relies on boundary integral equations for the adatom fluxes responsible for step flow. By applying asymptotics, which effectively treat the diffusive term of the free boundary problem as a singular perturbation, we describe an intimate connection of universal character between step kinetics and local geometry.

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“…Eq. (24). Subsequently, we scale all length scales and spatial coordinates of our system by this R 0 ; alternatively, set R 0 = 1 = L throughout.…”

Section: A On the Numerical Validation Of Our Approximationsmentioning

confidence: 99%