Performance of Piezoelectric MEMS Microphones

This semester project deals with the study of at fully clamped plates with various geome- tries (circular and square), piezoelectric properties and uniformly distributed load (normal to the surface). The stress distribution is analyzed in order to obtain an electrical displacement. The objective is to distinguish positive and negative stresses areas in our plate in order to dene an area for current measurements for microphone applications. For the circular plate, a straightforward analytical resolution of the problem is presented. For the square plate, the method of study is carried out mainly using the Galerkin method combined with the help of the symbolic algebraic software, Mathematica. The de ection of the plates is expressed in a series of polynomials which satisfy the homogeneous boundary conditions. Mathematica is used to solve for the coecients and generating the trial functions. The stress of the plate is then determined. Then the results obtained are compared with the exact solution obtained with the use of the nite element analysis software, Ansys. The results obtained from the Galerkin method show good agreement with those from Ansys. Finally, the obtained stresses functions are analyzed to determine their positive/negative domains.