The Analysis Of Vibration Frequency Of Film Bulk Acoustic Resonators

The wireless communication technology demands for RF components of smaller size, high frequency, high performance, low energy consumption, and low cost. Film bulk acoustic resonators (FBAR) are the latest technology offering RF components of small size and high frequency to the fast growing personal wireless communication technology.With the sophistication of the FBAR technology and demands for precision products, it is natural to make use of the full analysis of acoustic waves propagating in FBAR structures for design and calculating electrical parameters before the fabrication. Based on the justified assumption that the layered microstructure of FBAR can also be treated as infinite plates, vibration frequencies of the thickness-extension and thickness-shear vibration modes are calculated from layered models with perfectly bonded interfaces. A transcendental equation is used to determine the vibration frequency with given materials and plate thicknesses. By expanding the formulation to include the piezoelectric effect, we shall also be able to obtain the electrical field as a vital addition to mechanical vibration solutions. Of course, the piezoelectric effect will also be included in the frequency and displacements. The solutions can be used to calculate the electrical circuit parameters of a resonator.For electrical circuit parameters, the introduction of material viscosity will enable the formulation and calculation of FBAR properties with solutions of wave propagation. One approach to treat material viscosity is to assume the elastic constants as complex constants, in which the real part is the elastic constant and the imaginary part is the viscosity that is related to the frequency. In the mean time, the governing equations should be kept unaltered. However, since the viscosity constants of the film material are not available, so the viscosity of each material can be assumed to enable the calculation of the electrical parameters. The results can be compared with the measured electrical parameters, such as the quality factor. Then, a reasonable estimation of the viscosity of the film meterials can be obtained.The theoretical approach we present here will provide the first step for precise estimation of the thickness and electrical parameters so as to obtain the design frequecy. Of course, these one-dimensional formulation based on the infinite plate assumption can be further improved through the consideration of finite plates and numerical solutions based on the commonly used finite element analysis.