Model and Observations of Dielectric Charge in Thermally Oxidized Silicon Resonators

This paper investigates the effects of dielectric charge on resonant frequency in thermally oxidized silicon resonators hermetically encapsulated using ??epi-seal.?? SiO₂ coatings are effective for passive temperature compensation of resonators but make the devices more susceptible to charging-related issues. We present a theoretical model for the electromechanical effects of charge trapped in the dielectrics within the transduction gap of a resonator. Observations of resonance frequency against varying resonator bias voltage are fitted to this model in order to obtain estimates for the magnitude of the trapped oxide charge. Statistics collected from wet- and dry-oxidized devices show that lower fixed oxide charge can be expected upon dry oxidation. In addition, observations of time-varying resonator frequency indicate the presence of mobile oxide charge in a series of voltage biasing and temperature experiments.