On nanowire morphological instability and pinch-off by surface electromigration

¹ Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA
² Applied Physics Institute, Western Kentucky University, Bowling Green, KY 42101, USA

^* Corresponding author: mikhail.khenner@wku.edu

Received: 11 November 2024
Accepted: 20 February 2025

Abstract

Surface diffusion and surface electromigration may lead to a morphological instability of thin solid films and nanowires. In this paper two nonlinear analyses of a morphological instability are developed for a single-crystal cylindrical nanowire that is subjected to an axial current. These treatments extend the conventional linear stability analyses 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 pinching singularity of a cylinder radius, which leads to a wire separation into a disjoint segments. The time- and electric field-dependent dimensions of the focusing self-similar amplitude profile approaching a blow-up are characterized via the scaling analysis. Also, 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.