VHF single-crystal silicon elliptic bulk-mode capacitive disk resonators-part I: design and modeling

This work, the first of two parts, presents the design and modeling of VHF single-crystal silicon (SCS) capacitive disk resonators operating in their elliptical bulk resonant mode. The disk resonators are modeled as circular thin-plates with free edge. A comprehensive derivation of the mode shapes and resonant frequencies of the in-plane vibrations of the disk structures is described using the two-dimensional (2-D) elastic theory. An equivalent mechanical model is extracted from the elliptic bulk-mode shape to predict the dynamic behavior of the disk resonators. Based on the mechanical model, the electromechanical coupling and equivalent electrical circuit parameters of the disk resonators are derived. Several considerations regarding the operation, performance, and temperature coefficient of frequency of these devices are further discussed. This model is verified in part II of this paper, which describes the implementation and characterization of the SCS capacitive disk resonators.