Micromechanical IBARs: Modeling and Process Compensation

Manufacturability is a major challenge before widespread adoption of micromechanical resonators as frequency references. In this paper, the limits of frequency accuracy for a silicon resonator are investigated. The factors to these limits, including starting materials and process variations, are investigated. Design for manufacturing utilizing process compensation (PC) is presented. The I-shaped bulk acoustic resonator (IBAR) is considered since it has features that enable PC. A lumped-element model for the IBAR is developed. Assuming that variations in resonator geometry are locally systematic, the effect of process bias on resonator frequency is modeled. A procedure to obtain low sensitivity to process variations is explained. Process bias variation (i.e., skew) on a 10-MHz design is replicated with electron beam lithography. PC of a micromechanical resonator, confirmed with experimental data, is demonstrated for the first time. From the observations, strategies for obtaining absolute single-digit ppm frequency accuracy are presented.