Correction: Corrigendum: Quantum Limit of Quality Factor in Silicon Micro and Nano Mechanical Resonators

TLDR

Micromechanical resonators are promising replacements for quartz crystals as timing and frequency references because they can be compact, CMOS‑integrated, low‑cost, and low‑power, but their quality factor is ultimately limited by material properties, geometry, and operating conditions. The study aims to achieve high quality factors in resonators for high‑performance reference applications. The authors analyze the physics underlying the quantum limit of the Q‑f product, outline design strategies to reduce other dissipation sources, and report new results from resonators approaching this limit. Recent bulk‑acoustic resonators have been shown to operate near the quantum mechanical limit of the Q‑f product.

Abstract

Micromechanical resonators are promising replacements for quartz crystals for timing and frequency references owing to potential for compactness, integrability with CMOS fabrication processes, low cost, and low power consumption. To be used in high performance reference application, resonators should obtain a high quality factor. The limit of the quality factor achieved by a resonator is set by the material properties, geometry and operating condition. Some recent resonators properly designed for exploiting bulk-acoustic resonance have been demonstrated to operate close to the quantum mechanical limit for the quality factor and frequency product (Q-f). Here, we describe the physics that gives rise to the quantum limit to the Q-f product, explain design strategies for minimizing other dissipation sources, and present new results from several different resonators that approach the limit.