Theoretical potential of extremely high quality factors of β-Ga₂O₃ based MEMS resonators

We show theoretically and via simulation that β-Ga₂O₃ semiconductor is potentially a superior material for mechanical resonating structures applicable to micro-electro-mechanical system sensors. In particular, β-Ga₂O₃ may enable a thermoelastic dissipation loss limited quality factor on order of 10⁸, which is the highest among all known conductive materials including metals and semiconductors. The Akhiezer limit of the quality factor and frequency product of resonators based on β-Ga₂O₃ is predicted to be extremely high at 3.3 × 10¹⁵ Hz. β-Ga₂O₃ based resonators may even exhibit higher quality factors than those based on ultra-low expansion glass due to the elimination of metal electrodes in the former. We also present a method to graphically extract the quality factor from the frequency response function without measuring the FWHM bandwidth.