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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
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Abstract |
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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 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
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Mathematical Subject Classification 2010
Primary: 35R37, 35Q74, 37N15, 65Z05, 74H55
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Milestones
Received: 28 January 2015
Revised: 8 July 2015
Accepted: 31 July 2015
Published: 6 July 2016
Communicated by Natalia Hritonenko
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Authors |
| Aaron Wingo | |
| Department of Mathematics and
Statistics Eastern Kentucky University 521 Lancaster Avenue Richmond, KY 40475 United States |
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| Selahittin Cinar | |
| Department of Mathematics University of Houston 4800 Calhoun Road Houston, TX 77004 United States |
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| Kurt Woods | |
| General Motors Corporation Bowling Green, KY 42101 United States |
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| Mikhail Khenner | |
| Department of Mathematics Western Kentucky University 1906 College Heights Boulevard Bowling Green, KY 42101 United States |
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