Scaling of dissipation in megahertz-range micromechanical diamond oscillators

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.