#### Vol. 9, No. 4, 2016

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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 $h\left(x,t\right)$ 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