Modelling the Effect of Manufacturing Tolerances on the Performance of a MEMS Resonator

Date of Award


Publication Type


Degree Name



Mechanical, Automotive, and Materials Engineering

First Advisor



Microelectromechanical system resonator, Semiconductor-based fabrication, Etching, Fabrication tolerance, Micro-resonators



Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Microelectromechanical systems (MEMS) combine electrical components with mechanical systems on a micro scale. MEMS devices involve miniature micron-size mechanical moving structures manufactured using semiconductor-based fabrication. Deep reactive ion etching (DRIE) of silicon is widely used in MEMS device fabrication. Etching often involves creating narrow but deep trenches. It is one of the most popular fabrication techniques due to its flexibility between anisotropic and isotropic etching and high selectivity. However, the DRIE-based fabrication technique often has significant challenges, mainly from manufacturing process variations that lead to microstructure variations and induce various fabrication tolerances. However, these multiple tolerances, such as slanted etched profiles, DRIE scallops, and undercuts, can be avoided if the process focuses on a subset of features. This thesis presents numerical and analytical modeling techniques to understand the performance effect of slanted etched profiles, thickness, and undercut effects on frequency shifts in a reference model of micro-resonators, The analytical modeling result of the reference model was 726.86 Hz, while numerical analysis with 310,000 number of meshes reveals 772 Hz. The result of numerical calculation shows that increasing the angle of etch profile from 89° to 91° at the thickness of 60 μm, reduces the frequency response from 875.37 Hz to 650.22 Hz. Also, the result shows that for the case of 90° etch profile, the thickness of the structural layer has no influence on the frequency response. For other angles of etch profile, the thickness has an influence on the frequency. The undercut has a significant effect on the frequency response. For example, when the thickness of the structural layer is 60μm and angle of etch profile is 90°, changing the undercut from 0 μm to 4 μm resulted in the frequency changing from 770.33 Hz to 26.168 Hz.