Experimental and theoretical study of quartz and InP piezoelectric MEMS resonators

Abstract

<p>MEMS resonators, cantilevers and bridges, using the piezoelectric effect to drive and detect the fundamental resonance mode are studied. Two types of MEMS resonators are investigated in detail: a conventional quartz tuning fork (a two terminal device) and an InP bridge (a three terminal device). While the former is fabricated commercially from an insulating piezoelectric material the latter is fabricated via the controlled growth of a III-V semiconductor material with a non-zero piezoelectric coefficient. To utilize piezoelectricity based on a III-V semiconductor, an In_0.85Ga_0.15P /InP heterojunction was fabricated resulting in a depletion width which can be controlled using Schottky contacts. The result of this design is a piezoelectric device, in principle allowing for (dc) tuning of the magnitude of the resonant (ac) deflection and current. The type of deformation of interest is flexural and based on this a general theory relating the bending moment produced due to the piezoelectric stress is presented. Using this bending moment a general expression for the expected deflection and charge is derived analytically. For the quartz case the general expression, which has not been previously derived, is compared to the results of experiments and finite element simulations with good agreement. For the case of InP devices a resonance was not detected. This is attributed to the small piezoelectric coefficient of InP, the stiff bridge design that was chosen and large parasitic effects combining to make it difficult to observe the resonance. The fundamental mechanical noise of the quartz tuning fork was measured and is due to thermal fluctuations at the measurement temperature (~300K) associated with the dissipation in the mechanical system and can be related to the effective resistance of the resonator in the equivalent electrical circuit. Additionally, contributions to the package or dielectric capacitance using two and three terminal setups were studied. The three terminal configuration results in a lower package or dielectric capacitance than for the two terminal configuration.</p>