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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 and the finite element method (FEM). Resonance frequency values obtained by the analytical solution of the equation of motion and FEM analysis were compared and reasonable agreement showed validity of the FEM results. A resonance frequency close to 31.964 kHz was aimed 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. Based on FEM design, actual tuning fork crystals were fabricated using photolithography and oblique evaporation by a stencil mask. The average resonance frequency of the fabricated tuning fork samples at a vacuum level of 3 × 10  –2  torr was 31.228 to 31.462 kHz. The discrepancy between FEM modeling and observed values of resonance frequency is attributed to error in exactly manufacturing tuning fork tine width by photolithography. However, design parameters affecting other crystal parameters have to be adjusted comprehensively to optimize the tuning fork performance.

international journal of materials research

Development of SMD 32.768 kHz tuning fork-type crystals: Part lI: Analytical and finite element method design of quartz tuning fork resonators and experimental test of samples manufactured using photolithography