Calculating capacitance and analyzing nonlinearity of micro-accelerometers by Schwarz–Christoffel mapping

Designing micro-accelerometers requires the calculation of their capacitance. An analytical method based on the Schwarz–Christoffel mapping is proposed for the calculation of the capacitance of two types of micro-accelerometer, which enables the fringe effect to be taken into account. The two types of micro-accelerometer consist of four identical asymmetric comb-capacitors that produce a differential capacitance. For the micro-accelerometer without a handle layer under the comb-capacitor, only a single unit needs solving because the asymmetric comb-capacitor is composed of identical units. The analytical formula for the asymmetric comb-capacitor is verified by the three-dimensional finite element method. Through finite element method, the analytical formula is also extended to include asymmetric comb-capacitors of silicon-on-glass micro-accelerometers. A comparison between theoretical and experimental results from silicon-on-glass micro-accelerometers indicates the validity of the analytical formula. Based on the analytical formula, the nonlinearity of the micro-accelerometers is studied, which indicates that the high ratio between the wide and narrow gap distances can increase the linearity of micro-accelerometers.