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Recently an innovative mSpeaker technology, based on a novel kind of CMOS compatible small gap electrostatic actuators for large deflection, has been introduced [1]. In this paper, we devise methods to model such speakers in terms of lumped parameters using the deflection of the beam centre as sole dynamic variable. Optical, acoustical and finite element methods (FEM) are used to validate the non-linear lumped parameter model (LPM). The experimental evaluation and LPM simulations of the total harmonic distortion reveal deeper insights into the mechanisms governing linearity.
In der Arbeitsgruppe integrierte Siliziumsysteme des Fraunhofer IPMS werden am Standort Cottbus innovative Anwen-dungen eines neuartigen nanoskopischen elektrostatischen Antriebs (nanoskopic electrostatic drive – NED) untersucht. Eine der vielversprechendsten Anwendungen sind Lautsprecher. Vollständig aus Silizium gefertigte MEMS-Lautsprecher auf Basis von NED-Biegeaktoren werden vor den akustischen Messungen mechanisch und elektrisch cha-rakterisiert. Beidseitig eingespannte elektrostatisch betriebene in-plane NED-Aktoren werden dabei über einen Fre-quenzbereich von 20 Hz bis 20 kHz angeregt. Dabei sind die Strukturen oft verdeckt, was ihre Charakterisierung er-schwert. Es werden zerstörungsfreie optische Methoden präsentiert, mit deren Hilfe die Bestimmung der mechanischen Schwingungseigenschaften einzelner Aktoren ermöglicht wird sowie die Beweglichkeit im verdeckten Zustand nach-gewiesen werden kann.
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.