Simulation of Thin-Film Damping and Thermal Mechanical Noise Spectra for Advanced Micromachined Microphone Structures

In many micromachined sensors the thin (2-10 μm thick) air film between a compliant diaphragm and backplate electrode plays a dominant role in shaping both the dynamic and thermal noise characteristics of the device. Silicon microphone structures used in grating-based optical-interference microphones have recently been introduced that employ backplates with minimal area to achieve low damping and low thermal noise levels. Finite-element based modeling procedures based on 2-D discretization of the governing Reynolds equation are ideally suited for studying thin-film dynamics in such structures which utilize relatively complex backplate geometries. In this paper, the dynamic properties of both the diaphragm and thin air film are studied using a modal projection procedure in a commonly used finite element software and the results are used to simulate the dynamic frequency response of the coupled structure to internally generated electrostatic actuation pressure. The model is also extended to simulate thermal mechanical noise spectra of these advanced sensing structures. In all cases simulations are compared with measured data and show excellent agreement-demonstrating 0.8 pN/√Hz and 1.8 μPa/√Hz thermal force and thermal pressure noise levels, respectively, for the 1.5 mm diameter structures under study which have a fundamental diaphragm resonance-limited bandwidth near 20 kHz.