  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.
