Vol. 9, No. 4, 2016

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ISSN: 1944-4184 (e-only)
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Mathematical modeling of a surface morphological instability of a thin monocrystal film in a strong electric field

Aaron Wingo, Selahittin Cinar, Kurt Woods and Mikhail Khenner

Vol. 9 (2016), No. 4, 623–638
Abstract

A partial differential equation (PDE)-based model combining the effects of surface electromigration and substrate wetting is developed for the analysis of the morphological instability of a monocrystalline metal film in a high temperature environment typical to operational conditions of microelectronic interconnects and nanoscale devices. The model accounts for the anisotropies of the atomic mobility and surface energy. The goal is to describe and understand the time-evolution of the shape of the film surface. The formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the electric field is presented, followed by the results of the linear stability analysis of a planar surface. Computations of a fully nonlinear evolution equation are presented and discussed.

Keywords
nonlinear evolution PDEs, electromigration, surface diffusion, morphology, stability
Mathematical Subject Classification 2010
Primary: 35R37, 35Q74, 37N15, 65Z05, 74H55
Milestones
Received: 28 January 2015
Revised: 8 July 2015
Accepted: 31 July 2015
Published: 6 July 2016

Communicated by Natalia Hritonenko
Authors
Aaron Wingo
Department of Mathematics and Statistics
Eastern Kentucky University
521 Lancaster Avenue
Richmond, KY 40475
United States
Selahittin Cinar
Department of Mathematics
University of Houston
4800 Calhoun Road
Houston, TX 77004
United States
Kurt Woods
General Motors Corporation
Bowling Green, KY 42101
United States
Mikhail Khenner
Department of Mathematics
Western Kentucky University
1906 College Heights Boulevard
Bowling Green, KY 42101
United States