Model and Observations of Dielectric Charge in Thermally Oxidized Silicon Resonators

Modeling the effect of mobile ion contamination on the stability of a microelectromechanical resonator

“…2(b). 5 In Fig. 3 we present a comparison between the simulated and measured behavior of the resonance frequency during alternating DC-bias voltage stress between 16 and 20 V. The simulated and measured resonant frequencies are in excellent agreement.…”

“…From this observation, Bahl et al deduced that there must be some driving force other than the electric field. 5 Naturally, our explanation for the other driving force is the diffusion of mobile ions. At equilibrium at constant temperature, where the net-ion flux is zero (j ¼ 0 at all x), the concentration profile of the mobile charge only depends on the applied DC-bias voltage.…”

“…We compare theoretical results to the experimental results of Bahl et al 5 in the case of an oxidized silicon MEM resonator. Figure 1 shows the structure that is employed in the analysis of the mobile charge on a moving plate capacitor system.…”

“…In these resonators the built-in voltage can be determined from the DC-bias dependence of the resonant frequency. 5,9 The flux of mobile ions, j, can be calculated using the drift-diffusion theory and the time dependence of the mobile ion concentration, which is given by the continuity equations,…”

“…However, recent experiments by Bahl et al demonstrate that a mobile charge can cause a resonant-frequency drift in an oxidized silicon resonator under a relatively low electric field. 5 The resonant-frequency drift is one of the major barriers to the commercialization of silicon MEM resonators for timing applications. 6,7 Since the contamination is almost inevitable at present, it seems reasonable to also assume that mobile charge contamination can be a significant source of drift in other capacitive MEM components, such as voltage references 8 and accelerometers, which normally operate at lower electric fields than RF-MEM switches.…”