Modelling approach for MEMS transducers with rectangular clamped plate loaded by a thin fluid layer

Modeling of MEMS Transducers with Perforated Moving Electrodes

“…Due to the symmetry of the transducer’s geometry, the solution of ( 14 ) for nonuniform is expressed here in the first quadrant only (namely, ). The chosen Green’s function used in the integral formulation for the solution of ( 14 ) satisfies the same Neumann’s condition (the first derivative vanishes) at as the solution for the acoustic pressure, which can be expressed as follows [ 26 , 27 , 29 ]: with the Green’s function being given by with where denotes the cylindrical Hankel function of the second kind of order “0”.…”

“…The displacement field can be searched for in the following form of series expansion (with some truncation in practical implementation): where the orthonormal eigenfunctions satisfy the homogeneous equation associated with Equation ( 30 ): where . An approximate form of such eigenfunctions can be obtained as a series expansion over known functions from numerically (FEM) calculated results using the method described in [ 31 ] for nonperforated rectangular clamped plates and in [ 32 ] for perforated square clamped plates, the latter being used herein (see Appendix A ).…”

“…In the same reference, the acoustic pressure in the air gap was expressed using integral formulation with appropriate Green’s function, which was not expressed as a series expansion over the eigenfunctions of the moving electrode. Such a fomulation is also advantageous in the case of rectangular geometries [ 26 , 27 ] and is therefore used herein. It is worth mentioning the numerical methods, namely, the finite element method, which can take into account the thermoviscous losses and the coupling effects without geometry-dependent approximations [ 28 ].…”

“…Since no exact analytical expression for the eigenfunctions of perforated plates is known, to our knowledge, the eigenfunctions used in Section 2.3.2 are approximated using the series expansion [ 32 ] where the basis functions are the symmetrical eigenfunctions of 1D beam clamped at both ends, given by [ 27 , 35 ] and similarly for . Such a form of the basis functions ensures that the approximated eigenfunctions verify the boundary conditions ( 31 ).…”

A Low-Cost Fabrication and Numerical Simulation of a MEMS Acoustic Transducer Using Polyimide Membrane on FR4 Substrate

“…13 A two-dimensional transducer covering a rectangular or square shaped plate loaded using a fluid gap enclosed by peripheral cavity was designed. 14 A MEMS-based piezoelectric thin film based acoustic transducer was discussed. 15 A microphone was developed using silicon on insulator (SOI)-based wafer substrate.…”