Wafer-Level-Based Open-Circuit Sensitivity Model from Theoretical ALEM and Empirical OSCM Parameters for a Capacitive MEMS Acoustic Sensor

Abstract

We present a simple, accurate open-circuit sensitivity model based on both analytically calculated lumped and empirically extracted lumped-parameters that enables a capacitive acoustic sensor to be efficiently characterized in the frequency domain at the wafer level. Our mixed model is mainly composed of two key strategies: the approximately linearized electric-field method (ALEM) and the open- and short-calibration method (OSCM). Analytical ALEM can separate the intrinsic capacitance from the capacitance of the acoustic sensor itself, while empirical OSCM, on the basis of one additional test sample excluding the membrane, can extract the capacitance value of the active part from the entire sensor chip. FEM simulation verified the validity of the model within an error range of 2% in the unit cell. Dynamic open-circuit sensitivity is modelled from lumped parameters based on the equivalent electrical circuit, leading to a modelled resonance frequency under a bias condition. Thus, eliminating a complex read-out integrated circuit (ROIC) integration process, this mixed model not only simplifies the characterization process, but also improves the accuracy of the sensitivity because it considers the fringing field effect between the diaphragm and each etching hole in the back plate.