Effect of Electromigration on Onset of Morphological Instability of a Nanowire

TL;DR

This paper models the electromigration-induced morphological instability in nanowires, providing analytical solutions and numerical analysis to predict conditions leading to wire breakup or stabilization, with implications for nanowire fabrication.

Contribution

It extends existing models by incorporating electromigration effects and analyzes stability under various electric field strengths and contact angles.

Findings

Stronger electric fields increase instability growth rate.

Reversing electric field polarity can suppress instability.

Critical electric field value for wire stabilization is identified.

Abstract

Solid cylindrical nanowires are vulnerable to a Rayleigh-Plateau-type morphological instability. The instability results in a wire breakup, followed by formation of a chain array of spherical nanoparticles. In this paper, a base model of a morphological instability of a nanowire on a substrate in the applied electric field directed along a nanowire axis is considered. Exact analytical solution is obtained for 90 degrees contact angle and, assuming axisymmetric perturbations, for a free-standing wire. The latter solution extends the 1965 result by Nichols and Mullins without electromigration effect (F.A. Nichols and W.W. Mullins, Trans. Metall. Soc. AIME 233, 1840-1848 (1965)). For general contact angles the neutral stability is determined numerically. It is shown that a stronger applied electric field (a stronger current) results in a larger instability growth rate and a decrease of the most dangerous unstable wavelength; in experiment, the latter is expected to yield more dense chain array of nanoparticles. Also it is noted that a wire crystallographic orientation on a substrate has larger impact on stability in a stronger electric field and that a simple switching of the polarity of electrical contacts, i.e. the reversal of the direction of the applied electric field, may suppress the instability development and thus a wire breakup would be prevented. A critical value of the electric field that is required for such wire stabilization is obtained.