Does greater piezo-resistive transduction give rise to higher anchor loss in a square-extensional mode micromechanical resonator?

The square-extensional (SE) mode resonator was used as the timing element in one of the first demonstrations of a MEMS oscillator meeting the GSM specification for phase noise. Crucial to its high Q was the use of T-shaped tethers in the anchoring design, which could also be used as piezo-resistors that could provide higher transduction. In this work, we examine the relationship between Q and corresponding piezo-resistive transduction efficiency, affected by changes in the compliance of the T-shaped tether anchoring design. Does a high Q necessarily mean a lower piezo-resistive transduction factor as an unavoidable performance tradeoff? Our measurement results, corroborated by finite element simulations, suggest that Q and the related piezo-resistive transduction factor are not opposed to each order in the SE mode resonator. In fact, the two indicative metrics of performance exhibit similar trends to the other with respect to changing the compliance of the anchoring design.