Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 4 (2016), 623-638.

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

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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 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.

Article information

Involve, Volume 9, Number 4 (2016), 623-638.

Received: 28 January 2015
Revised: 8 July 2015
Accepted: 31 July 2015
First available in Project Euclid: 22 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R37: Moving boundary problems 35Q74: PDEs in connection with mechanics of deformable solids 37N15: Dynamical systems in solid mechanics [See mainly 74Hxx] 65Z05: Applications to physics 74H55: Stability

nonlinear evolution PDEs electromigration surface diffusion morphology stability


Wingo, Aaron; Cinar, Selahittin; Woods, Kurt; Khenner, Mikhail. Mathematical modeling of a surface morphological instability of a thin monocrystal film in a strong electric field. Involve 9 (2016), no. 4, 623--638. doi:10.2140/involve.2016.9.623.

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