Quartz resonator for MEMS oscillator

A three-dimensional length-extension mode (3D-LEM) resonator has been developed for fundamental physics purpose showing a very good frequency stability potential highlighted by a Quality factor Frequency product (Q.F) above 1013. Those characteristics are quite interesting for time & frequency applications but since a 3D structure is difficult to integrate, a planar two-dimensional (2D) resonator approach is now undertaken. Because of the intrinsic quartz high quality factor and good thermal stability, this new resonator shall be able to challenge silicon resonator based MEMS oscillator with comparable dimensions. It will furthermore respond to the need for simple collective machining and flat pack packaging. This paper focuses on the theoretical study of this new 2D-LEM resonator. The first part is about defining the best geometric compromises and mounting area designs to meet high quality factor requirements. This was made through Finite Element Modeling (FEM). Two quartz cut oriented perpendicular to X and Z crystallographic axes have been compared with adapted actuation electrodes systems to analyze the thermal sensitivity and the motional resistance thanks to the OOFELIE Multiphysics FEM software. An estimate of the phase noise level is also presented. To collectively process such small resonators Deep Reactive Ion Etching (DRIE) on quartz wafer bonded substrates is currently being developed.