Effect of electromigration on onset of morphological instability of a nanowire

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 \(90^\circ \) 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 (Nichols and Mullins in Surface-(Interface-) and volume-diffusion contributions to morphological changes driven by capillarity. 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.