Scaling of dissipation in megahertz-range micromechanical diamond oscillators

TL;DR

This study investigates how frequency and energy loss in micromechanical diamond oscillators depend on device size, revealing different dissipation mechanisms dominate at different scales and confirming theoretical scaling laws.

Contribution

It provides empirical scaling laws for frequency and dissipation in diamond resonators, identifying clamping and surface losses as primary dissipation sources.

Findings

Frequency scales as 1/L^2, confirming thin-beam approximation.

Clamping loss dominates in shorter beams.

Surface losses are significant in longer beams.

Abstract

We report frequency and dissipation scaling laws for doubly-clamped diamond resonators. The device lengths range from 10 microns to 19 microns corresponding to frequency and quality-factor ranges of 17 MHz to 66 MHz and 600 to 2400 respectively. We find that the resonance frequency scales as 1/L^2 confirming the validity of the thin-beam approximation. The dominant dissipation comes from two sources; for the shorter beams, clamping loss is the dominant dissipation mechanism; while for the longer beams, surface losses provide a significant source of dissipation. We compare and contrast these mechanisms with other dissipation mechanisms to describe the data.