Electrostatic Generation of Bulk Acoustic Waves and Electrical Parameters of Si-MEMS Resonators

This paper proposes an analytical approach to model the generation of bulk acoustic waves in an electrostatically excited silicon MEMS structure, as well as its electromechanical response in terms of static and dynamic displacements, electromechanical coupling, and motional current. The analysis pertains to the single-port electrostatic drive of trapped-energy thickness-extensional (TE) modes in thin plates. Both asymmetric single-side and symmetric double-side electrostatic gap configurations are modeled. Green's function is used to describe the characteristic of the static displacement of the driven surface of the structure versus the dc bias voltage, which allows us to determine the electrical response of the resonator. Optical and electrical characterizations have been performed on resonator samples operating at 10.3 MHz on the fundamental of TE mode under single-side electrostatic excitation. The various figures of merit depend on the dc bias voltage. Typical values of 9000 for the Q-factor, and of 10
^-5
for the electromechanical coupling factor k
²
have been obtained with V
_DC
≈ 50 V for 1-μ-thick gaps. Here-considered modes have a typical temperature coefficients of frequency (TCF) close to -30 ppm/°C. We conclude that the practical usability of such electrostatically excited bulk acoustic waves (BAW) resonators essentially depends on the efficiency of the compensation of feed-through capacitance.