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We investigate the effect of free electrons on the quality factor (Q) of ametallic nanomechanical resonator in the form of a thin elastic beam. Theflexural and longitudinal modes of the beam are modeled using thin beamelasticity theory, and simple perturbation theory is used to calculate the rateat which an externally excited vibration mode decays due to its interactionwith free electrons. We find that electron-phonon interaction significantlyaffects the Q of longitudinal modes, and may also be of significance to thedamping of flexural modes in otherwise high-Q beams. The finite geometry of thebeam is manifested in two important ways. Its finite length breaks translationinvariance along the beam and introduces an imperfect momentum conservation lawin place of the exact law. Its finite width imposes a quantization of theelectronic states that introduces a temperature scale for which there exists acrossover from a high-temperature macroscopic regime, where electron-phonondamping behaves as if the electrons were in the bulk, to a low-temperaturemesoscopic regime, where damping is dominated by just a few dissipationchannels and exhibits sharp non-monotonic changes as parameters are varied.This suggests a novel scheme for probing the electronic spectrum of a nanoscaledevice by measuring the Q of its mechanical vibrations.

Damping of mechanical vibrations by free electrons in metallic nanoresonators