RAHERISON

The Legendre polynomial method has been extended to the modeling of MEMS resonator disc with current excitation (equicharge current source). Formulation is given that allows the electric current source to be taken into account. A unique formalism has been developed which allows for both harmonic and modal analyses. Numerical results such as normalized electric input impedance, resonant and anti-resonant frequencies, dispersion curves and displacement profiles are presented and compared with those obtained by using voltage excitation in order to check the accuracy and range of applicability of the proposed approach.

This work presents the modeling of high contrast partially electroded resonators by means of a polynomial approach. This method allows easily solving the equations that govern the structure. The boundary, symmetry, and continuity conditions are automatically incorporated into the equations of motion by the use of delta functions for the variables stress (T) and electric displacement (D) and appropriate analytical expression forms for the independent variables, mechanical displacements (u), and electric potential (ϕ). Structure symmetry was used to reduce the number of unknowns. For the zinc oxide (ZnO) resonator in extreme geometrical cases (thin plate and bar cases), a good agreement was obtained between the results of the proposed polynomial approach and those of an analytical approach for both the modal and harmonic analyses. The proposed polynomial approach was used to calculate the 2D resonator electrical admittance (full and partial metallization) near the 1D thickness fundamental mode, and the results highlight the presence of spurious modes. Influence of the metallization rate on the number of spurious modes in the bandwidth is studied. This model can also easily calculate the electromechanical coupling coefficient and the field profiles. Illustrations for both electromechanical coupling coefficient and particle displacement profiles are given for aluminium nitride (AlN), lead zirconate titanate, and ZnO resonators.

The frequency spectrum of a piezoelectric hollow resonator cylinder is studied by using Legendre polynomials. Formulation is given that allows to take into account the electric source. Normal frequencies and electric input impedance are obtained easily regardless of the type of modes, thickness extensional (TE), thickness shear (TS), edge (E) or radial (R). These quantities are calculated as a function of the diameter to thickness ratio and the results are compared against other calculations from an analytical approach. The numerical results for harmonic and modal analyses such as normalized electric input impedance, the resonance and antiresonance frequencies are presented and compared with the analytical results in order to check the accuracy and range of applicability of the proposed approach. Agreement is obtained.

A mapped orthogonal functions technique is extended for solving three-dimensional acoustical wave problems with taking into account electrical sources. For validation and illustration purposes, it is applied to the determination of the frequency spectrum of a piezoelectric disc resonator. Formulation is given for the calculation of the electric input admittance along with specializations for open- and short-circuit boundary conditions. In view of validation, normal frequencies and electric input admittance are obtained for specific geometries where a one-dimensional analytical model is working and compared against results from the analytical approach. Illustrative results, dispersion curves for a PZT5A resonator and electromechanical coupling coefficients as a function of the diameter to thickness ratio for the first radial mode of a respectively PZT5A, AlN and SiC resonator are also given.

In this paper, we present a polynomial approach for determining the acoustic guided waves in homogeneous infinitely long cylinders using elastic materials of cylindrical anisotropy. The formulation is based on linear three-dimensional elasticity using an analytic form for the displacement field. The approach incorporates the stress-free boundary conditions directly into the equations of motion which are solved numerically by expanding each displacement component using Legendre polynomials and trigonometric functions. The problem is then reduced for anisotropic homogeneous structures to a tractable eigenvalue problem allowing the dispersion curves and associated profiles to be easily calculated. Numerical results of the guided waves for axisymmetric and flexural modes are presented and compared with those published earlier in order to check up the accuracy and range of applicability of the approach. The developed software proves to be very efficient to retrieve the guided waves of any nature and the modes of all orders. The computational advantages of the approach are described.

Legendre polynomial method which describes the structure and incorporates automatically the boundary conditions in constitutive and propagation equations is used to model acoustic wave cylindrical resonators. It is the first time this method is applied to study standing rather than propagative waves. The advantage of this approach is, in a unique formulation, to take into account electric sources. The analytical and numerical resolutions are presented to highlight the potentialities of the Legendre polynomial approach. The vibration characteristics of piezoelectric discs with regard to diameter to thickness D/H ratios are analyzed by the three dimensional modeling approach through both modal and harmonic analyses. Resonance and antiresonance frequencies, electric input impedance, dispersion curves, field profiles and electromechanical coupling coefficient, easily obtained, are presented for PZT5A resonator piezoelectric discs. To validate our approach, the results using our 3D polynomial modelling of acoustic wave resonator are compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the radial modes of all orders.

A bidimensional analysis of 6 mm hexagonal resonators is described using a double orthonormal basis set for the expansion of field quantities. The analysis takes into account the electrical voltage source and by means of a unique formalism along with a single calculation restitutes all the types of resonance whatever the thickness to width ratio value through either modal solutions or electrical impedance. An illustrative example gives the capabilities of the method to investigate spurious modes in laterally bounded resonators.

Radio-Frequency electro-acoustic resonators and filters are key components for wireless communication devices. The next generation of mobile systems requires for these components a strict size reduction, higher operating frequency and better power resistance. So, MEMS BAW (Bulk Acoustic Wave) devices have emerged as an efficient alternative to established Surface Acoustic Wave filtering solutions. Knowledge of the electromechanical coupling coefficient and the Q-factor are of primary importance for the MEMS BAW device design. In our model, the Legendre polynomial method which describes the structure and incorporates automatically the boundary conditions in constitutive and propagation equations is used to calculate these parameters. It is the first time this method is applied to study standing rather than propagative waves. The advantage of this approach are, in a unique formulation, to take into account the presence of sources, existence of electrodes' losses and dissimilarity of the constituent materials of the resonator. To validate this approach, it is applied to a Al/ZnO/Al resonator. Through harmonic and modal analysis, the influence of electrodes properties on MEMS BAW resonator performances are illustrated; the results are compared with those published earlier. This method is an efficient tool for designing MEMS BAW filter.