Analysis of film thickness dependence on electrical equivalent model for AT-cut resonators

This paper describes the theoretical analysis and experiment regarding film thickness dependence on an electrical equivalent model for AT-Cut resonators. Resonant frequencies were 10 MHz for fundamental waves vibrating in thickness shear C-modes. Measurements for electrical equivalent circuit constant characteristics versus film thickness were conducted by using a network analyzer. An equivalent model for film thickness plated on AT-Cut resonators in the neighborhood of resonance frequency was proposed and analyzed. By using the experimental frequency temperature characteristics, a quadric relationship between frequency turn-over temperatures and film thickness was also obtained. It was found that these theoretical and experimental results could be very useful in designing AT-Cut resonators, among other things