28 February 2005 Finite-difference-based dynamic modeling of MEMS bridge
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In this paper, we present a finite difference based one-dimensional dynamic modeling, which includes electro-thermal coupled with thermo-mechanical behavior of a multi-layered micro-bridge. The electro-thermal model includes the heat transfer from the joule-heated layer to the other layers, and establishes the transient temperature gradient through the thickness of the bridge. The thermal moment and axial load resulting from the transient temperature gradient are used to couple electro-thermal with thermo-mechanical behavior. The dynamic modeling takes into account buckling, and damping effects, asymmetry residual stresses in the layers, and lateral movement at the support ends. The proposed model is applied to a tri-layer micro-bridge of 1000μm length, made of 2μm silicon dioxide sandwiched in between 2μm thick epi-silicon, and 2μm thick poly silicon, with four 400μm long legs, and springs at the four corners the bridge. The beam, and legs are 40μm, and 10μm wide respectively. Results demonstrate the bi-stability of the structure, and a large movement of 40μm between the up and down stable states can easily be obtained. Application of only 21mA electrical current for 15μs to the legs is required to switch buckled-up position to buckled-down position. An additional trapezoidal waveform electrical current of 100mA amplitude for 4μs, and 100μs falling time needs to be applied for the reverse actuation. The switching speed in both cases is less than 500μs.
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Aron Michael, Aron Michael, Kevin Yu, Kevin Yu, Chee Yee Kwok, Chee Yee Kwok, } "Finite-difference-based dynamic modeling of MEMS bridge", Proc. SPIE 5649, Smart Structures, Devices, and Systems II, (28 February 2005); doi: 10.1117/12.582404; https://doi.org/10.1117/12.582404

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