Behavioral Modeling and Simulation of MEMS Electrostatic and Thermomechanical Effects

This thesis extends and updates the N__qodal Design of Actuators and Sensors (NODAS) library previously developed at Carnegie Mellon University. NODAS is a library of atomic element lumped parameter behavioral models written in Verilog-A, an analog hardware description language (AHDL). It is used for the simulation of MEMS devices in a SPICE-like circuit simulator. Physics modeling, accuracy verification, and application examples are presented. The modeling of 2D beams and 2D electrostatic gaps for MEMS devices is presented in this thesis, however, the physics can be extended to 3D. The NODAS beam model was updated and new physical effects were added. The inconsistent use of a user parameter which caused the length of the beam to be miscalculated was corrected. A new variable was created to address this problem and verification of the NODAS beam model compared with analytic equations. When compared to analytic equations for a fixed-fixed beam under a uniform distributed load and a fixed-guided beam with axial compressive stress under a uniform distributed load, the NODAS beam model was shown to be accurate to within 6.1 xl 0.6 percent and 15xl 0-3 percent respectively when using multiple NODAS beam segments. The moment generated by the differences between the thermal coefficients of expansion in a multi-layer CMOSMEMS beam was implemented. A multi-layer CMOS-MEMS beam under an applied temperature was simulated in NODAS and ANSYS. The NODAS simulation reported in-plane tip deflections to within 2% of the ANSYS simulation for different metal layer combinations and offsets. A thermal conduction model was added to account for the effects of electrothermal heating. The electromechanical gap model was updated and an electric-only gap model was created. A electrostatically actuated fixed-fixed beam simulation using electromechanical gap models was shown to produce beam deflections to within 2.2% of an ANSYS simulation when 128 NODAS beam/gap segments were used. The electric-only gap model was created to reduce the simulation time of large models such as an RF MEMS varactor. A thermal actuator, a varactor, and a mixer application example are given to demonstrate composability and hierarchical design. Finally, future areas of research are discussed.