ELECTROSTATICALLY DRIVEN VACUUM-ENCAPSULATED POLYSILICON RESONATORS .2. THEORY AND PERFORMANCE

In this paper, the design, modelling and performance characteristics o f electrostatically driven vacuum-encapsulated polysilicon resonators are addressed. A one-port configuration is preferably employed for exc itation and detection of the vibration. Mechanical instability (pull-i n) is discussed on the basis of the energy minimum principle. An expre ssion for the pull-in voltage of a beam is given. The electromechanica l behaviour in a limited frequency regime around the fundamental reson ance is accurately modelled by an electric circuit consisting of a (st atic) capacitor shunted by a series (dynamic) RLC branch. The d.c. bia s dependence of the circuit components and of the series resonance fre quency has been experimentally investigated and is compared with the t heory. The large-amplitude behaviour is discussed as well. The plate m odulus and residual strain of boron-doped polysilicon are estimated fr om the resonance frequencies of microbridges of varying lengths. The f easibility of their application as resonant strain gauges is investiga ted. The 210 mu m long beams typically have an unloaded fundamental fr equency of 324 kHz, a gauge factor of 2400 and an uncompensated temper ature coefficient of -135 ppm degrees C-1.