Direct parameter extraction in feedthrough-embedded capacitive MEMS resonators

Abstract

This paper presents a method for fast and accurate determination of parameters relevant to the characterization of capacitive MEMS resonators like quality factor ( Q), resonant frequency ( f n ), and equivalent circuit parameters such as the motional capacitance ( C m ). In the presence of a parasitic feedthrough capacitor ( C F ) appearing across the input and output ports, the transmission characteristic is marked by two resonances: series ( S) and parallel ( P). Close approximations of these circuit parameters are obtained without having to first de-embed the resonator motional current typically buried in feedthrough by using the series and parallel resonances. While previous methods with the same objective are well known, we show that these are limited to the condition where C F ≪ C m Q. In contrast, this work focuses on moderate capacitive feedthrough levels where C F > C m Q, which are more common in MEMS resonators. The method is applied to data obtained from the measured electrical transmission of fabricated SOI MEMS resonators. Parameter values deduced via direct extraction are then compared against those obtained by a full extraction procedure where de-embedding is first performed and followed by a Lorentzian fit to the data based on the classical transfer function associated with a generic LRC series resonant circuit.