Frequency-temperature analysis of MEMS AT-cut quartz resonators

An analytical study of the frequency-temperature behavior of MEMS AT-cut quartz resonator structures was performed. The piezoelectric, Lagrangian equations for the frequency-temperature behavior of quartz were employed. Two types of resonator structures were studied: A 1 GHz rectangular plate with rectangular electrodes and a 1 GHz rectangular ring electrode mesa (REM) plate. For MEMS resonators, the REM design confers certain advantages in attaining higher resonant frequencies and lower electrode noise.