Scaling analysis of capacitive MEMS microphones considering residual stress

We conduct a systematic scaling analysis of the sensitivity of a silicon capacitive MEMS microphone based on a dimensionless 1-degree-of-freedom (1DOF) model considering residual stress. The theoretical normalized sensitivity we derived is a nonlinear function of normalized diaphragm size (h/a), acoustic driving frequency, 3 effective stiffness terms and the other parameters. From our 1DOF model, the optimal normalized diaphragm has to be trade-off between high sensitivity and large bandwidth. In addition, we found that a critical diaphragm radius of 415 μm for a silicon MEMS microphone, is located at the inflection point in the sensitivity function of the radius. In addition, this critical radius corresponds to the minimum effective stiffness of the microphone.