Superimposed STM images of the six stable rotation stations of a DMBI-P molecule during a step by step clockwise rotation induced by voltage pulses (V = 0.5 V, I = 0.5 nA, t = 10 s).

Electrostatic micromechanical actuators have numerous applications in science and technology. In many applications, they are operated in a narrow frequency range close to resonance and at a drive voltage of low variation. Recently, new applications, such as microelectromechanical systems (MEMS) microspeakers (µSpeakers), have emerged that require operation over a wide frequency and dynamic range. Simulating the dynamic performance under such circumstances is still highly cumbersome. State-of-the-art finite element analysis struggles with pull-in instability and does not deliver the necessary information about unstable equilibrium states accordingly. Convincing lumped-parameter models amenable to direct physical interpretation are missing. This inhibits the indispensable in-depth analysis of the dynamic stability of such systems. In this paper, we take a major step towards mending the situation. By combining the finite element method (FEM) with an arc-length solver, we obtain the full bifurcation diagram for electrostatic actuators based on prismatic Euler-Bernoulli beams. A subsequent modal analysis then shows that within very narrow error margins, it is exclusively the lowest Euler-Bernoulli eigenmode that dominates the beam physics over the entire relevant drive voltage range. An experiment directly recording the deflection profile of a MEMS microbeam is performed and confirms the numerical findings with astonishing precision. This enables modeling the system using a single spatial degree of freedom.

Electrostatic actuators are of particular interest for microsystems (MEMS), and in particular for MEMS audio transducers for use in advanced true wireless applications. They are attractive because of their typically low electrical capacitance and because they can be fabricated from materials that are compatible with standard complementary metal-oxide semiconductor (CMOS) technology. For high audio performance and in particular low harmonic distortion (THD) the implementation of the push-pull principle provides strong benefits. With an arrangement of three electrodes in a conjunct moving configuration on a beam, we demonstrate here for the first time a balanced bending actuator incarnating the push-pull principle operating at low voltages. Our first design already exhibits a harmonic distortion as low as 1.2% at 79 dB using a signal voltage of only 6 Vp and a constant voltage of only ±10 Vdc in a standard acoustic measurement setup. Thus, exceeding our previously reported approach in all three key performance indications at the same time. We expect that our novel electrode configurations will stimulate innovative electrostatic actuator developments for a broad range of applications. In this paper we report the basic theory, the fabrication and the performance of our novel actuator design acting as an audio transducer.

This article presents a circuit model that is able to capture the full nonlinear behavior of an asymmetric electrostatic transducer whose dynamics are governed by a single degree of freedom. Effects such as stressstiffening and pull-in are accounted for. The simulation of a displacement-dependent capacitor and a nonlinear spring is accomplished with arbitrary behavioral sources, which are a standard component of circuit simulators. As an application example, the parameters of the model were fitted to emulate the behavior of an electrostatic MEMS loudspeaker whose finite-element (FEM) simulations and acoustic characterisation where already reported in the literature. The obtained waveforms show good agreement with the amplitude and distortion that was reported both in the transient FEM simulations and in the experimental measurements. This model is also used to predict the performance of this device as a microphone, coupling it to a two-stage charge amplifier. Additional complex behaviors can be introduced to this network model if it is required.

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