Fabrication and characterization of thermally actuated micromechanical resonators for airborne particle mass sensing: I. Resonator design and modeling

This paper, the first of two parts, presents a comprehensive electro-thermo-mechanical modeling of thermally actuated in-plane single crystalline silicon MEMS resonators. The resonator structures have been particularly chosen for high-precision measurement of unevenly distributed added masses of airborne particles and high tolerance of air viscous damping. Thermal-piezoresistive transduction has been chosen for the resonators in this work for its robustness against contaminations and airborne particles, as well as fabrication simplicity. However, the operation and electrical equivalent model of such resonators has barely been explored. Analysis and modeling of such resonators is more sophisticated than capacitive or piezoelectric resonators as it includes electrical, thermal and mechanical mechanisms and interactions between them. A combination of finite element analysis, analytical derivations and numerical methods has been utilized in this work to develop the electrical equivalent model of such devices. The modeling strategy developed here can be applied to thermally actuated micromechanical resonators with a variety of other topologies. Fabrication and characterization of the resonators and mass measurement of airborne particles using such resonators is presented in the second part of this paper.