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From crater functions to partial differential equations: a new approach to ion bombardment induced nonequilibrium pattern formation

Scott A Norris, Michael P Brenner and Michael J Aziz

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We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in terms of the moments of the crater function. We demonstrate that the formalism reproduces the classical Bradley–Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. Given an actual set of converged molecular dynamics moments and their derivatives with respect to the incidence angle, our approach can be applied directly to predict the presence and absence of surface morphological instabilities. This analysis represents the first work systematically connecting molecular dynamics simulations of ion bombardment to partial differential equations that govern topographic pattern-forming instabilities.


PACS

68.35.B- Structure of clean surfaces (and surface reconstruction)

68.49.Sf Ion scattering from surfaces (charge transfer, sputtering, SIMS)

02.30.Jr Partial differential equations

79.20.Rf Atomic, molecular, and ion beam impact and interactions with surfaces

Subjects

Mathematical physics

Condensed matter: electrical, magnetic and optical

Surfaces, interfaces and thin films

Dates

Issue 22 (3 June 2009)

Received 11 February 2009

Published 12 May 2009



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