Analytical and finite element method design of quartz tuning fork resonators and experimental test of samples manufactured using photolithography 1—significant design parameters affecting static capacitance C0

Abstract

Resonance frequency of quartz tuning fork crystal for use in chips of code division multiple access, personal communication system, and a global system for mobile communication was analyzed by an analytical method, Sezawa’s theory and the finite element method (FEM). From the FEM analysis results, actual tuning fork crystals were fabricated using photolithography and oblique evaporation by a stencil mask. A resonance frequency close to 31.964 kHz was aimed at following FEM analysis results and a general scheme of commercially available 32.768 kHz tuning fork resonators was followed in designing tuning fork geometry, tine electrode pattern and thickness. Comparison was made among the modeled and experimentally measured resonance frequencies and the discrepancy explained and discussed. The average resonance frequency of the fabricated tuning fork samples at a vacuum level of 3×10 −2 Torr was 31.228–31.462 kHz. The difference between modeling and experimentally measured resonance frequency is attributed to the error in exactly manufacturing tuning fork tine width by photolithography. The dependence of sensitivities for other quartz tuning fork crystal parameter C 0 on various design parameters was also comprehensively analyzed using FEM and Taguchi’s design of experiment method. However, the tuning fork design using FEM modeling must be modified comprehensively to optimize various design parameters affecting both the resonance frequency and other crystal parameters, most importantly crystal impedance.