Electrostatically driven vacuum-encapsulated polysilicon resonators

Abstract

In this paper, the design, modelling and performance characteristics of electrostatically driven vacuum-encapsulated polysilicon resonators are addressed. A one-port configuration is preferably employed for excitation and detection of the vibration. Mechanical instability (pull-in) is discussed on the basis of the energy minimum principle. An expression for the pull-in voltage of a beam is given. The electromechanical behaviour in a limited frequency regime around the fundamental resonance is accurately modelled by an electric circuit consisting of a (static) capacitor shunted by a series (dynamic) RLC branch. The d.c. bias dependence of the circuit components and of the series resonance frequency has been experimentally investigated and is compared with the theory. The large-amplitude behaviour is discussed as well. The plate modulus and residual strain of boron-doped polysilicon are estimated from the resonance frequencies of microbridges of varying lengths. The feasibility of their application as resonant strain gauges is investigated. The 210 m long beams typically have an unloaded fundamental frequency of 324 kHz, a gauge factor of 2400 and an uncompensated temperature coefficient of-135 ppm 'C-'.

Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces

“…For convenience, we introduce the nondimensional variables (denoted by hats) (5) where t ͂ is a time scale, as defined below. Substituting equation (5) into equation (4) and dropping the hats, we obtain (6) The nondimensional parameters appearing in equation (6) are…”

“…The pull-in voltage of this microbeam based on a static analysis [7,27] is 0.652 V, and accounting for the transient effect it is 0.6 V. Figure 11(a) shows the time response of the microbeam when actuated by a voltage load V dc = 0.36 V and subjected to a mechanical shock pulse of amplitude 400 g and duration 1.0 ms. Here, W max /d is the maximum deflection of the microbeam at x = L normalized to d, and t is the nondimensional time, as defined in (5). It turns out that the first natural period of the microbeam is much smaller than the pulse duration, and hence the microbeam experiences the mechanical shock as a quasi-static load.…”

Free Vibration of Geometrically Nonlinear Functionally Graded Micro-switches under Electrostatic Force and Temperature Change

“…To validate the present analysis, the first natural frequency of C-C micro-beams is compared with experimental results provided by Tilmans and Legtenberg [2]. The micro-beam is made of pure poly-silicon in the validation example, and the Young's modulus E = 151 GPa.…”

“…Counteracting the electrostatic force is the elastic force, which tries to restore the movable electrode to its original position. Meanwhile, an instantaneous excitation will induce free vibration of the micro-beam at the deflected state and the natural frequencies of the system are influenced by the static deflection [2][3][4].…”

Measuring and interpreting the mechanical–thermal noise spectrum in a MEMS

“…If the device is overdamped and a step voltage, V step , slightly higher than the static pull-in [9], is applied to the structure (V step = αV pi , with 1 < α < 1.1), a pull-in motion characterized by a meta-stable region is observed (figure 2).…”