The Rapid Analytical-FEA Technique for Reduced Simulation Times of Piezoelectric MEMS Resonators

Abstract

Piezoelectric radio frequency microelectromechanical resonators are a promising technology for meeting the increasing demands of a crowded electromagnetic spectrum. Contour mode resonators are a potential technology for next generation filtering to replace current bulk acoustic wave (BAW) solutions. The lithographically defined center frequencies of contour mode resonators facilitate monolithic integration of multiple frequencies on a single chip, ideal for filter bank applications. Despite these advantages, contour mode resonator technology has not seen widespread use in commercial or military applications, with one of the main obstacles towards this end being spurious mode. Frequently, designs optimally exciting an intended mode will often excite many other modes. This can affect important performance metrics, such as the passband roll-off and group delay of filters created from these resonators, and potentially exposes the radio system to damaging high power signals. Part of the reason spurious modes remain a challenge is the lack of a rapid and wide-band simulation technique. Piezoelectric resonators typically have complex responses that must be modeled using finite element analysis (FEA) for accuracy. Conventionally, a Multiphysics harmonic analysis is run to model resonators. These simulations can take hours to days to complete. Trades must be made between frequency spacing and bandwidth for the simulation to complete in a reasonable amount of time, and can possibly miss modes. Due to the time limitations, designers often run 2D simulations which complete much faster, but will miss any out-of-plane information. To address these challenges, the wide-band Rapid Analytical-FEA Technique (RAFT) has been developed using software commonly found in research laboratories. The RAFT combines the speed of analytical analysis with the accuracy of FEA for full 3D solutions that complete orders of magnitude faster than conventional harmonic analysis while accurately modeling relevant modes. This enhanced speed is enabled by generalized expressions for the motional parameters of the modified Butterworth van-Dyke equivalent circuit: the motional resistance (Rm), inductance (Lm), and capacitance (Cm). Information from separate mechanical modal analysis and electrostatic analysis are entered into these expressions, and the frequency response is then simulated in analytical software. This accounts for the effect of all modes in the simulation bandwidth. This method is shown to improve simulations speeds by several orders of magnitude. Additionally, the RAFT enables new uses of FEA for design and analysis. Wide band simulations to assess the resonator performance far from resonance are now possible. Accurate parametric device exploration to investigate mode scaling and behavior to higher frequencies can be undertaken. The reduced simulation duration frees time for researchers to conduct studies of other critical device variables, such as the simulations of fabrication non-idealities, including electrode misalignment or sidewall angles. These effects are often not simulated due to time constraints. Thermal effects on frequency may be included to generate frequency-temperature curves for each mode’s unique response to temperature variations.