Piezoresistive Readout Mechanically Coupled Lamé Mode SOI Resonator With $Q$ of a Million

This paper describes the use of the coupling beam in a pair of mechanically coupled Lamé mode resonators to enhance electromechanical transduction by piezoresistive sensing, while at the same time maintaining a high quality factor of a million. This corresponds to an fQ product of 1.3 × 10
¹³
, which approaches the Akhiezer limit of silicon. With a 15 mA bias current, electrical characterization of the array using the piezoresistive readout via the coupling-beam provides a 25 dB enhancement over a single Lamé mode resonator using capacitive readout. In this paper, we have modeled the piezoresistive electromechanical frequency response function of the device both analytically and by finite elements. The models mutually agree and are experimentally verified by measured results of fabricated resonators. The model indicates that the transduction factor is independent of the lateral dimensions and thickness of the resonator.