Small signal modeling of charge and piezoresistive modulations in active MEM resonators

In this work we establish novel analytical and small signal circuit modeling of two major effects that co-exist in active micro-electro-mechanical resonators: charge and piezoresistance modulations. Analytical expressions for the output current of vibrating body field effect transistors including capacitive, FET and piezoresistive current components are established and an equivalent small signal circuit is validated experimentally. Two design cases of vibrating FETs are studied and analyzed in detail: (i) a 2 MHz flexural mode resonator operating in a charge-dominant modulation, (ii) a 30 MHz bulk mode resonator operating with significant piezoresistive modulation. Proposed models are able to accurately predict device transfer characteristics at resonance and the influence of various bias levels and configurations.