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April 2014
David Tumpold
Modeling and Optimization Methods of an Electrostatically driven MEMS Speaker
The market for battery powered devices, such as smart-phones or tablets increases rapidly. The trend goes towards smaller and thinner cases. The main challenge is to decrease the power consumption by coincidently shrinking the device size and increasing the efficiency. Micro-electro-mechanical-systems (MEMS) manufactured of silicon, merge cost effective and space saving features as an energy efficient and innovative product. In this work, reversible operated silicon microphones are modeled and optimized towards sound pressure level and total harmonic distortion. The models are described by coupled partial differential equations and solved by the help of the finite element method. Due to the small dimensions of a single acoustic transducer of approximately one millimeter in diameter and two micrometer in thickness, the loudspeaker is manufactured as an eight bit array. The array arrangement opens up the opportunity to drive the speaker in conventional analog driving mode or apply digital sound reconstruction. Geometric nonlinearities such as large deformation, pre-stress or mechanical contact are reflected in the mechanical model and excited electrostatically. By applying the virtual displacement method, the influence of the insulation layer is mapped to the electrostatic force computation. The electrostatic force interacts with the structural mechanics and the membrane starts to oscillate. The electrostatically actuated membrane is coupled to the acoustic model, where the sound pressure level is computed. The challenge in the acoustic propagation computation is on the one hand, the number of unknowns, which can be minimized by using Mortar FEM (non-conforming grids), and on the other hand, in the reflections caused by the bounds of truncating the propagation region. These reflections are minimized with absorbing boundary conditions or a perfectly matched layer surrounding the propagation region. Acoustic results on the single transducer were computed by the finite element method, where for the full speaker array a specially developed wave field computation software was used based on the Kirchhoff-Helmholtz integral. In addition, two optimization strategies towards increasing the sound pressure level were presented. The first deals with stress-induced self raising of the back plate structure, to increase the volume flow and sound pressure level. The second deals with the digital sound reconstruction, investigating the non-reset, with-reset and latched method.
Keywords: MEMS; Simulation; Modeling; Electrostatic; Speaker; Acoustic
Measurement-, Actuator-, and Simulation-Technology
Edited by Univ.Prof. Dipl.-Ing. Dr.techn. Manfred Kaltenbacher, Wien
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DOI 10.2370/9783844026979
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