19 April 2002 Modeling methodology for a CMOS-MEMS electrostatic comb
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Proceedings Volume 4755, Design, Test, Integration, and Packaging of MEMS/MOEMS 2002; (2002) https://doi.org/10.1117/12.462801
Event: Symposium on Design, Test, Integration, and Packaging of MEMS/MOEMS 2002, 2002, Cannes-Mandelieu, France
A methodology for combined modeling of capacitance and force 9in a multi-layer electrostatic comb is demonstrated in this paper. Conformal mapping-based analytical methods are limited to 2D symmetric cross-sections and cannot account for charge concentration effects at corners. Vertex capacitance can be more than 30% of the total capacitance in a single-layer 2 micrometers thick comb with 10 micrometers overlap. Furthermore, analytical equations are strictly valid only for perfectly symmetrical finger positions. Fringing and corner effects are likely to be more significant in a multi- layered CMOS-MEMS comb because of the presence of more edges and vertices. Vertical curling of CMOS-MEMS comb fingers may also lead to reduced capacitance and vertical forces. Gyroscopes are particularly sensitive to such undesirable forces, which therefore, need to be well-quantified. In order to address the above issues, a hybrid approach of superposing linear regression models over a set of core analytical models is implemented. Design of experiments is used to obtain data for capacitance and force using a commercial 3D boundary-element solver. Since accurate force values require significantly higher mesh refinement than accurate capacitance, we use numerical derivatives of capacitance values to compute the forces. The model is formulated such that the capacitance and force models use the same regression coefficients. The comb model thus obtained, fits the numerical capacitance data to within +/- 3% and force to within +/- 10%. The model is experimentally verified by measuring capacitance change in a specially designed test structure. The capacitance model matches measurements to within 10%. The comb model is implemented in an Analog Hardware Description Language (ADHL) for use in behavioral simulation of manufacturing variations in a CMOS-MEMS gyroscope.
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Sitaraman V. Iyer, Sitaraman V. Iyer, Hasnain Lakdawala, Hasnain Lakdawala, Tamal Mukherjee, Tamal Mukherjee, Gary K. Fedder, Gary K. Fedder, } "Modeling methodology for a CMOS-MEMS electrostatic comb", Proc. SPIE 4755, Design, Test, Integration, and Packaging of MEMS/MOEMS 2002, (19 April 2002); doi: 10.1117/12.462801; https://doi.org/10.1117/12.462801

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