Mechanical modeling of mesa-diaphragm structures in microelectromechanical systems

A mechanical model of mesa-diaphragm structures was used to test the mechanical characteristics of microstructures. The diaphragm was approximated by an infinitely long thin plate embossed in the center. A formula deduced using the theory of plates and shells related the mesa elastic modulus, thickness and cross-sectional area to the surface stress distribution at the diaphragm. The formula was confirmed by finite-element simulations. The results show that the equivalent flexural rigidity of the mesa-diaphragm structure increases with increasing elastic modulus and mesa thickness. Therefore, the strength of the compound structure can be increased by increasing the elastic modulus and mesa thickness. The analytical model provides a method to optimize the design of mesa-diaphragm structures.