Design Guidelines for Thin Diaphragm-Based Microsystems through Comprehensive Numerical and Analytical Studies

Abstract

This paper presents comprehensive guidelines for the design and analysis of a thin diaphragm that is used in a variety of microsystems, including microphones and pressure sensors. It highlights the empirical relations that can be utilized for the design of thin diaphragm-based microsystems (TDMS). Design guidelines developed through a Finite Element Analysis (FEA) limit the iterative efforts to fabricate TDMS. These design guidelines are validated analytically, with the assumption that the material properties are isotropic, and the deviation from anisotropic material is calculated. In the FEA simulations, a large deflection theory is taken into account to incorporate nonlinearity, such that a critical dimensional ratio of 𝑎/ℎ or 2𝑟/ℎ can be decided to have the linear response of a thin diaphragm. The observed differences of 12% in the deflection and 13% in the induced stresses from the analytical calculations are attributed to the anisotropic material consideration in the FEA model. It suggests that, up to a critical ratio (𝑎/ℎ or 2𝑟/ℎ), the thin diaphragm shows a linear relationship with high sensitivity. The study also presents a few empirical relations to finalize the geometrical parameters of the thin diaphragm in terms of its edge length or radius and thickness. Utilizing the critical ratio calculated in the static FEA analysis, the basic conventional geometries are considered for harmonic analyses to understand the frequency response of the thin diaphragms, which is a primary sensing element for microphone applications, and many more. This work provides a solution for microelectromechanical system (MEMS) developers to reduce cost and time while conceptualizing TDMS designs.