  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.
