Pressure effects on the dissipative behavior of nanocrystalline diamond microelectromechanical resonators

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Diamond-based microelectromechanical resonators have the potential of enhanced performance due to the chemical inertness of the diamond structural layer and its high Young’s modulus, high wear resistance, low thermal expansion coefficient, and very high thermal conductivity. In this work, the resonance frequency and quality factor of MEMS resonators based on nanocrystalline diamond films are characterized under different air pressures. The dynamic behavior of 50–300 μm long linear bridges and double ended tuning forks, with resonance frequencies between 0.5 and 15 MHz and quality factors as high as 50 000 are described as a function of measurement pressure from high vacuum(~10 mTorr) up to atmospheric conditions. The resonance frequencies and quality factors in vacuum show good agreement with the theoretical models including anchor and thermoelastic dissipation (TED). The Young’s moduli for nanocrystalline diamond films extrapolated from experimental data are between 840–920 GPa. The critical pressure values, at which the quality factor starts decreasing due to dissipation in air, are dependent on the resonator length. Longer structures, with quality factors limited by TED and lower resonance frequencies, have low critical pressures, of the order of 1–10 Torr and go from an intrinsic dissipation, to a molecular dissipation regime and finally to a region of viscous dissipation. Shorter resonators, with higher resonance frequencies and quality factors limited by anchor losses, have higher critical pressures, some higher than atmospheric pressure, and enter directly into the viscous dissipation regime from the intrinsic region.