Nonlinear Dynamics of Metallic Nanofabrication

TL;DR

This paper derives a PDE model for metallic nanowire shape evolution incorporating electron-shell effects, revealing universal equilibrium shapes that explain experimental observations of cylindrical nanowires.

Contribution

It introduces a novel PDE model based on fluid dynamics concepts that captures the nonlinear dynamics of nanowire shape evolution including kink interactions.

Findings

Universal equilibrium shape of nanowires identified

Kink dynamics explain nanowire formation

Model aligns with experimental observations

Abstract

Using concepts from fluid dynamics, a partial differential equation for the shape evolution of a metallic nanowire is derived from a semiclassical energy functional that includes electron-shell effects. A rich dynamics, involving movement and interaction of kinks connecting locally stable radii, leads to the formation of a wire whose equilibrium shape is universal and consists of a cylindrical part connected to unduloid-like leads. The universality of the equilibrium shape may provide an explanation for the formation of cylindrical nanowires observed in recent experiments.