Island Dynamics and Level Set Methods for Continuum Modeling of Epitaxial Growth

Barry Merriman (), Russel Caflisch (), Stanley Osher (), Christian Ratsch (), Susan Chen (), Myungjoo Kang () and Mark Gyure ()
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Barry Merriman: UCLA, Department of Mathematic
Russel Caflisch: UCLA, Department of Mathematic
Stanley Osher: UCLA, Department of Mathematic
Christian Ratsch: UCLA, Department of Mathematic
Susan Chen: UCLA, Department of Mathematic
Myungjoo Kang: UCLA, Department of Mathematic
Mark Gyure: HRL Laboratories

A chapter in Applied and Industrial Mathematics, Venice—2, 1998, 2000, pp 145-171 from Springer

Abstract: Abstract Molecular Beam Epitaxy is a method for growing atomically thin films of material. During epitaxial growth, atoms are deposited on a surface, where they hop randomly until attaching at the edges of partially completed atomic monolayers. This process has practical application to the fabrication of high speed semiconductor electronic devices. We have formulated a new model for epitaxial growth, the “Island Dynamics Model”, in which the growth is described by the motion of the partial monolayer (“island”) boundaries, coupled to diffusive transport of the deposited atoms. This provides a continuum description in the lateral surface directions, but atomic scale discreteness in the surface height, which is well suited to the regime of practical interest. Level set methods are employed for computations based on this model. In this paper we give some elementary background on epitaxial growth, outline the Island Dynamics Model, review the Level Set Method, and discuss the novel level set techniques required in this application. We also present comparisons with two traditional models for epitaxial growth, Kinetic Monte Carlo simulations and Rate Equations.

Keywords: Epitaxial Growth; Deposition Flux; Capture Zone; Kinetic Monte Carlo; Thin Film Growth (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-011-4193-2_9

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DOI: 10.1007/978-94-011-4193-2_9

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