Compact Modeling of MEMS Resonators

The main accomplishment of this project was the development, for the first time, of a compact transient large-signal MEMS resonator model for large-scale integration of resonators and transistors. The four quarterly milestones, including electricalmechanicalthermal characterization, preliminary resonator model, electricalmechanicalthermal validation, and extended resonator model, were all met. MEMS cantilever resonators were fabricated at Nanyang Technological University in Singapore by using a novel low-temperature wafer bonding process to realize 3D features that could not be realized in a single silicon wafer. The simple and relatively large design facilitated model development and validation. Using well-known characteristics of silicon, only the thickness of the cantilever was fine-tuned to match the modeled and measured resonance frequencies. A compact transient large-signal resonator model was developed and coded in Verilog-A, so that it could be readily installed in different circuit-design environments such as ADS and Cadence. The effects of DC-bias and AC-drive levels and frequencies were simulated in both time and frequency domains. The model validation was mostly through mechanical characterization by using a laser Doppler vibrometer. Electrical validation was more difficult due to high leakage current associated with the silicon substrate. Thermal validation was inaccurate due to weak temperature dependence.