Damping of mechanical vibrations by free electrons in metallic nanoresonators

TL;DR

This paper explores how free electrons influence the damping and quality factor of metallic nanoresonators, revealing effects of electron-phonon interactions and finite geometry on vibrational decay.

Contribution

It introduces a perturbation theory approach to quantify electron-phonon damping in finite metallic nanobeams, highlighting the impact of geometry and electronic spectrum quantization.

Findings

Electron-phonon interaction significantly affects longitudinal mode damping.

Finite geometry causes non-monotonic temperature-dependent damping behavior.

Damping behavior varies between bulk-like and mesoscopic regimes depending on temperature.

Abstract

We investigate the effect of free electrons on the quality factor (Q) of a metallic nanomechanical resonator in the form of a thin elastic beam. The flexural and longitudinal modes of the beam are modeled using thin beam elasticity theory, and simple perturbation theory is used to calculate the rate at which an externally excited vibration mode decays due to its interaction with free electrons. We find that electron-phonon interaction significantly affects the Q of longitudinal modes, and may also be of significance to the damping of flexural modes in otherwise high-Q beams. The finite geometry of the beam is manifested in two important ways. Its finite length breaks translation invariance along the beam and introduces an imperfect momentum conservation law in place of the exact law. Its finite width imposes a quantization of the electronic states that introduces a temperature scale for which there exists a crossover from a high-temperature macroscopic regime, where electron-phonon damping behaves as if the electrons were in the bulk, to a low-temperature mesoscopic regime, where damping is dominated by just a few dissipation channels and exhibits sharp non-monotonic changes as parameters are varied. This suggests a novel scheme for probing the electronic spectrum of a nanoscale device by measuring the Q of its mechanical vibrations.