Dimension optimization of a MEMS LC pressure sensor

In this work, an analytical method is introduced to optimize the structure of a MEMS LC pressure sensor based on the device pressure range, the maximum overload pressure, and other design constraints. The method can be applied to square and circular membrane sensors. The sensitivity of the LC structure is directly proportional to the sensitivity of its capacitor. To obtain the maximum sensitivity for a MEMS capacitor, the maximum displacement of the membrane under the maximum allowed pressure is used to determine the gap size between two electrodes. The ultimate stress of the membrane under the maximum overload pressure would define the length over thickness ratio of the membrane. To optimize he size of the LC structure, the total sensor area must be minimized. For a given resonant frequency, there would be a tradeoff between the size of the inductor and the capacitor. As a case study, the optimization method is employed to optimize the structure of a pressure sensor with a pressure range of 0-100 psi and an overload pressure of 200 psi. The obtained optimum size for a square sensor is 2.2 mm and for a circular sensor is 2.5 mm.