Micromechanical resonator. (a) Wafer design: a 20 mm by 20 mm wafer of thickness 500 μm, with a pattern of three paddles on a 5 mm long torsion rod. (b) Optical microscope image of the central element of the resonator: a square mm paddle connected by torsion rods of length 0.5 mm and width 0.3 mm. (c) Finite element modelling view of the 3 paddles, each with a width of 1 mm and thickness 500 μm. Side paddles have a length of 1.8 mm. This design was chosen to obtain a torsional mode with high frequency and a central paddle to act as a rigid body.
Schematic drawing of the experimental setup. Brass columns (BC); PZT with a glued-on steel pyramidal tip; Focusing lens (FL). Red lines indicate the laser beam path. Black lines indicate the electronic connections. The sample is kept inside a vacuum tank, at room temperature.
Comparison of modelling and measured data for a low and high frequency mode. (a) Fundamental drum mode of the wafer expected at 10.64 kHz. (b) Observed amplitude distribution of angular vibration across the wafer at 10.7 kHz clearly demonstrates the acoustic energy is mostly on the wafer. (c) Torsional mode expected at 401.9 kHz. (d) Observed amplitude distribution of angular vibration at 401.5 kHz, where acoustic energy is concentrated on the central paddle. Measured frequencies agree with modelling predictions to within 400 Hz.
Observed quality factor of (7.5 ± 0.2) × 105 at a pressure of 10−3 Pa and room temperature. A ringdown curve is observed (red data points) when we switch off the fixed sinusoidal signal source at 401.5 kHz. The quality factor is calculated from the exponential fit (blue dashed line) of the ringdown, with error bar obtained from the standard deviation of multiple measurements.
Review of mechanical resonators reported in the literature with high quality factors and frequencies in the range of interest.
Comparison of the measured frequencies of mechanical modes at room temperature and pressure of 10−3 Pa to modelling predictions. Both resonator modes (401.5 and 296.2 kHz) have high quality factors (∼105), while both wafer modes (35.5 and 10.7 kHz) have low quality factors (∼103).
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