Self-Aligned Single-Electrode Actuation of Tangential and Wineglass Modes using PMN-PT

Considering evolution of rotation sensing and timing applications realized in Micro-electro-mechanical systems (MEMS), flexural mode resonant shapes are outperformed by bulk acoustic wave (BAW) counterparts by achieving higher frequencies with both electrostatic and piezoelectric transduction. Within the 1-30 MHz range, which hosts BAW gyroscopes and timing references, piezoelectric and electrostatic MEMS have similar transduction efficiency. Although, when designed intelligently, electrostatic transduction allows self-alignment between electrodes and the resonator for various BAW modes, misalignment is inevitable regarding piezoelectric transduction of BAW modes that require electrode patterning. In this paper transverse piezoelectric actuation of [011] oriented single crystal lead magnesium niobate-lead titanate (PMN-PT) thin film disks is shown to excite the tangential mode and family of elliptical compound resonant modes, utilizing a self-aligned and unpatterned electrode that spans the entire disk surface. The resonant mode coupling is achieved employing a unique property of [011] PMN-PT, where the in-plane piezoelectric coefficients have opposite sign. Fabricating 1-port disk transducers, RF reflection measurements are performed that demonstrate the compound mode family shapes in 1-30 MHz range. Independent verification of mode transduction is achieved using in-plane displacement measurements with Polytec's Laser Doppler Vibrometer (LDV). While tangential mode achieves 40$^o$/sec dithering rate at 335 kHz resonant frequency, the n=2 wine-glass mode achieves 11.46 nm tip displacement at 8.42 MHz resonant frequency on a radius of 60 $\mu $m disk resonator in air. A single electrode resonator that can excite both tangential and wine-glass modes with such metrics lays the foundation for a BAW MEMS gyroscope with a built-in primary calibration stage.