Behavioral modeling and simulation of micromechanical resonator for communications applications

Abstract

A method for modeling and simulating MEMS is presented for communications applications. This method includes the automatic generation of a simulation-ready description of the MEMS device including coupled electro-mechanical behavior extracted from a geometrical device description. In order to solve the lack of interoperability with simulators to perform MEMS analyses, the proposed method introduces a model output fully compatible with behavioral simulators such as those from Tanner Research/spl reg/, Mentor Graphics/spl reg/, Synopsys/spl reg/, Agilent Technologies/spl reg/ and Cadence/spl reg/ for electronic simulations. This paper especially focuses on how to integrate a coupled-electromechanical model in an RF simulator like ADS from Agilent. The complete design flow is presented including layout design, automatic 3D model generation for 3D analysis, behavioral model generation and integration of the component into a circuit simulation. Two methods are presented- automatic generation of an electrical equivalent circuit for the MEMS device and- a method creating a fully non-linear device model which can be used as a black box within the circuit simulation environment. The paper presents an example based on a 10-MHz micromechanical resonator embedded within a Pierce oscillator circuit following the work of Nguyen. The model of the micromechanical resonator, a clamped-clamped beam that vibrates in a vertical displacement in response to an electrostatic excitation, is automatically created following the complete flow described above. The resonator has been analyzed at two levels: the device- and the system-level. On one hand, the intrinsic mechanical properties are obtained with the finite element method. On the other hand, the behavioral- and electrical equivalent circuit-models are generated from the finite element model by reducing the number of degrees of freedom. The analysis of the oscillator circuit is then performed with several RF simulators. In Nguyen's work, the author has simulated the oscillator circuit using an RLC-equivalent model of the micromechanical resonator. In contrast to the method presented in Nguyen article, the inclusion of coupled electro-mechanical behavior model in a circuit level simulation allows the representation of the non-linear effects of the MEMS device. The simulation results, highly coherent with results obtained on the circuit that integrates the RLC-equivalent model, highlight this mechanical non-linearity.