Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies

Abstract

A PDE-based model combining surface electromigration and wetting is developed for the analysis of morphological stability of ultrathin solid films. Adatom mobility is assumed anisotropic, and two directions of the electric field (parallel and perpendicular to the surface) are discussed and contrasted. Linear stability analyses of small-slope evolution equations are performed, followed by computations of fully nonlinear parametric evolution equations that permit surface overhangs. The results reveal parameter domains of instability for wetting and non-wetting films and variable electric field strength, nonlinear steady-state solutions in certain cases, and interesting coarsening behavior for strongly wetting films.Submitted to the special issue "Nanoscale wetting of solids on solids" of the journal Comptes Rendus Physique (Olivier Pierre-Louis, Univ. Lyon, Editor)

Electromigration-driven Evolution of the Surface Morphology and Composition for a Bi-Component Solid Film

“…Notice that the derivatives of the diffusional mobilities are slaved to the electric field parameter F , in other words the anisotropy effect emerges only when the electromigration is operational [13,14,21]. A nontrivial solution of the algebraic system exists if and only if the determinants of the real and the imaginary parts of A both equal zero.…”

“…Surface electromigration [37] was studied theoretically in connection to the grain-boundary grooving in polycrystalline films [1]- [5], the kinetic instabilities of crystal steps [6]- [12], morphological stability of thin films [13]- [21], and recently, as a way to fabricate nanometer-sized gaps in metallic films -suitable for testing of the conductive properties of single molecules and control of their functionalities [22]- [24]. This paper theoretically investigates the effects of electromigration on morphological stability and evolution of a bi-component, atomically rough surface of a single-crystal metal or semiconductor film (a generic substitutional binary alloy or a non-reactive compound).…”

Untitled

“…It is this combination that makes adatoms drift. Surface electromigration was studied theoretically in connection to the grain-boundary grooving in polycrystalline films [Averbuch et al 2001;Maroudas 1995], the kinetic instabilities of crystal steps [Chang et al 2006;Debierre et al 2007;Stoyanov 1997], morphological stability of thin films [Dobbs and Krug 1994;Krug and Schimschak 1997;Barakat et al 2012;Khenner 2013], and recently, as a way to fabricate nanometer-sized gaps in metallic films -suitable for testing of the conductive properties of single molecules and control of their functionalities [Barnes et al 2010;Bolotin et al 2007;Block et al 2006]. Although the phenomenon of electromigration has been known for over 100 years, it became of practical interest MSC2010: 35R37, 35Q74, 37N15, 65Z05, 74H55.…”

“…Here we further develop the PDE-based mathematical model of the film-surface morphological instability and evolution driven by the electromigration [Khenner 2013]. The very special feature of the presented model is that it accounts both for the wetting and the surface energy anisotropy effects.…”

“…The very special feature of the presented model is that it accounts both for the wetting and the surface energy anisotropy effects. The surface morphological instability and evolution in a thin film system where the wetting, anisotropy, and electromigration are active have not been addressed theoretically, although PDE-based models of wetting and anisotropy [Davis et al 2004;Gill and Wang 2008;Khenner 2008a;2008b;Khenner et al 2011], wetting and electromigration [Khenner 2013], and electromigration and anisotropy [Barakat et al 2012] have been published.…”