ALEM-based dynamic modeling for a capacitive acoustic sensor

Abstract

An analytical modeling to enhance the accuracy of the dynamic open-circuit sensitivity is presented for a capacitive acoustic sensor in a microphone for mobile devices, especially a smart phone module. It can be done by considering the fringing field effect for etching holes of the back-plate not presented in the conventional works. The effective capacitor model of the capacitor with etching holes in the packaged microphone is obtained by applying the proposed approximately linearized electric-field method (ALEM), which enables to extract the static open-circuit sensitivity due to its relationship linked to the transduction area in the acoustic domain. Consequently, the dynamic sensitivity modeling based on the ALEM-based capacitor and the static open-circuit sensitivity are conducted. In addition, to verify the accuracy, the proposed modeling is analyzed and compared with both the finite element method (FEM) simulated capacitance and the conventional equivalent circuits. The modeling process is largely divided into three steps: ALEM-based capacitor modeling, the static open-circuit sensitivity modeling, and the dynamic open-circuit sensitivity modeling. First of all, the modeling for the effective capacitor is performed. From the vector-notation based capacitor model, both the intrinsic capacitance in the active area and the capacitive attenuation factor were determined to 2.2 pF and 91.6 %, respectively, at the air-gap height of 1.1 ？m. The discrepancy for the proposed analytical capacitor model compared to those of FEM simulation was less than 1.7 %, showing the validation of the model. Secondly, the static open-circuit sensitivity of the capacitive acoustic sensor is modeled. The characterization with the two test patterns: the sensor test pattern without the membrane and without the active area. With the pull-in voltage of 12.0 V and the pad capacitance of 0.23 pF, the air-gap height is modeled as a function of the voltage, where the residual stress of the diaphragm was extracted to 23.0 MPa, leading to the effective spring constant of 190 N/m. Lastly, the performance is characterized in the frequency domain. The dynamic open-circuit sensitivity modeled on the basis of the static open-circuit sensitivity and the ALEM-based capacitor model was determined to -38.9 dBV/Pa at 1 kHz at the bias voltage of 10 V, indicating a difference of 1.1 dB in comparison to that of the conventional model with the overestimated effect of the parasitic capacitance. The analytical model in hand calculation with two test patterns was proposed and investigated to model the dynamic open-circuit sensitivity of a capacitive acoustic sensor. It is obvious that the model considering the fringing field effect for etching holes of the back-plate can improve the modeling accuracy. Additionally, this advantage may be attractive for those involved in a sensor, ROIC as well as microphone module. Thus, these results demonstrate that the proposed modeling is suitable for the analytical modeling approach of a capacitive acoustic sensor.