Higher dimensional flexure mode for enhanced effective electromechanical coupling in PZT-on-silicon MEMS resonators

This paper reports on a low-loss, flexural-mode resonator with enhanced effective electromechanical coupling, k
_eff
²
. Improvement is achieved by utilizing a higher dimensional vibrational mode that possesses more than one non-zero, in-phase normal-stress component. Specifically, the stress profile augments coupling with contributions from both the d
₃₁
and d
₃₂
piezoelectric coefficients. The 52.6 MHz flexure-based mode of the 0.5-μm lead zirconate titanate (PZT) on 4-μm silicon resonator yields ~4x boost in k
_eff
²
(2.07% versus 0.55%) when compared with the fundamental length-extensional mode of the same device. Measurements also reveal a 50 Ω terminated insertion loss (IL) of -3.6 dB and motional resistance, R
_m
=45Ω despite an unloaded quality factor (Q
_UL
) of 122.