On Nanowire Morphological Instability and Pinch-Off by Surface Electromigration

Surface diffusion and surface electromigration may lead to a morphological instability of thin solid films and nanowires. In this paper two nonlinear analyzes of a morphological instability are developed for a single-crystal cylindrical nanowire that is subjected to the axial current. These treatments extend the conventional linear stability analyzes without surface electromigration, that manifest a Rayleigh-Plateau instability. A weakly nonlinear analysis is done slightly above the Rayleigh-Plateau (longwave) instability threshold. It results in a one-dimensional Sivashinsky amplitude equation that describes a blow-up of a surface perturbation amplitude in a finite time. This is a signature of a formation of an axisymmetric spike singularity of a cylinder radius, which leads to a wire pinch-off and separation into a disjoint segments. The scaling analysis of the amplitude spike singularity is performed, and the time-and-electric field-dependent dimensions of the spike are characterized. A weakly nonlinear multi-scale analysis is done at the arbitrary distance above a longwave or a shortwave instability threshold. The time-and-electric field-dependent Fourier amplitudes of the major instability modes are derived and characterized.