Finite Element-Based Analysis of Single-Crystal Si Contour-Mode Electromechanical RF Resonators

Micron-scale electromechanical disk-shaped resonators have exhibited operational frequencies above 1 GHz and quality factors exceeding 1,500 at these frequencies. Additionally, such disk resonators can be potentially realized in current silicon CMOS and BiCMOS integrated circuit processes, making them attractive alternatives to traditional high-Q off-chip components. Accurate modeling of these devices is critical to predicting the mode-shape and, most importantly, the vibration frequency. This paper presents a finite element-based approach to modeling higher-order effects in disk-shaped resonators using ANSYS 7.0. An in-depth study of the mode-shapes for disk resonators of various sizes, and the effects of substrate anchors attached to the disks at various locations, is included. Effects on resonator operation due to metal layers, such as electroless plated copper, deposited on the disks are also simulated. All simulations are performed in a fully coupled electrical-mechanical environment so as to incorporate as many process and excitation variables as possible.