Analytical Modeling, Design, and Performance Analysis of a Micromirror for Space-Based Multiobject Spectroscopy

This article presents the analytical modeling, design, and performance analysis of an electrostatic micromirror for space-based Multiobject Spectroscopy (MOS). The micromirror under investigation is a double-bridge design with hidden cantilevers architecture in which the deflection is achieved by a combination of bending and twisting cantilevers. A simple closed-form solution of pull-in voltage and deflection is obtained using the parallel-plate capacitor model that assumes micromirror deflection dominated by bending cantilevers due to electrostatic actuation. The design optimization is done to achieve a micromirror of size $200\,\,\mu \text{m}\,\,\times 200\,\,\mu \text{m}$ , deflection $2.5~\mu \text{m}$ , pull-in voltage smaller than 25 V, and a shock survival capacity of at least 10 000 g. The static and dynamic behavior of the optimized design is obtained using the analytical model and compared with the finite-element method (FEM) and characterization results and found to be in close agreement. The micromirror exhibits an analytical pull-in voltage near the FEM and measured pull-in voltage with a deviation of 5% and 0.9%, respectively. The analytical resonance frequency is also closer to simulation and measurement results with a deviation of 4.66% and 2.58%, respectively. The analytical switching time is also very close to the FEM results, with a deviation of 28%. The analytical model and the simple approach of design optimization using tuning parameters presented in the article can be used to design the micromirror according to desired specifications.