Fundamental Thickness Extensional Mode Research Articles

Energy Integration Method for Calculating k eff and its Application in Design Optimization of Disk Resonators via Convex Edge

Piezoelectric resonators have been extensively used as filters, actuator, and sensors. The effective electromechanical coupling coefficient ( [Formula: see text] is the most useful parameter to evaluate the electromechanical conversion efficiency of piezoelectric resonators. However, even for simple geometry piezoelectric resonators, such as disks, the coupling between different modes makes the resonant characteristics very complex. The coupling causes low electromechanical coupling efficiency of the intended mode. We propose a finite-element-based energy integration method to calculate [Formula: see text] of piezoelectric resonators. This method is more accurate than the conventional resonance-antiresonance method and provides a powerful tool for the design optimization of pure mode resonators. A special case studied here is the fundamental thickness extensional (TE) mode of PZT-8 disks in the aspect ratio range of 2-20. Our results showed that multimode coupling near this mode can be greatly suppressed by modifying the edge surface of the disk to a convex shape. Such an optimized design could enhance [Formula: see text] of the fundamental TE mode by as much as 10%-45% depending on the aspect ratio.

Electromechanical Anisotropy at the Ferroelectric to Relaxor Transition of (Bi0.5Na0.5)0.94Ba0.06TiO3 Ceramics from the Thermal Evolution of Resonance Curves

(Bi0.5Na0.5)0.94Ba0.06TiO3 dense ceramics were obtained from autocombustion sol-gel synthesized nanopowders and sintered at 1050 °C for 1–2 h for the study of the electromechanical anisotropy. Measurement of the complex impedance spectrum was carried out on thin ceramic disks, thickness-poled, as a function of the temperature from 16 °C up to the vanishing of the electromechanical resonances at the ferroelectric to relaxor transition near 100 °C. The spectrum comprises the fundamental radial extensional mode and three overtones of this, together with the fundamental thickness extensional mode, coupled with other complex modes. Thermal evolution of the spectrum shows anisotropic behavior. Piezoelectric, elastic, and dielectric material coefficients, including all losses, were determined from iterative analysis of the complex impedance curves at the planar, thickness, and shear virtually monomodal resonances of disks and shear plates, thickness-poled. d33 was measured quasi-statically at 100 Hz. This set of data was used as the initial condition for the optimization of the numerical calculation by finite elements of the full spectrum of the disk, from 100 kHz to 1.9 MHz, to determine the thermal evolution of the material coefficients. An appropriate measurement strategy to study electromechanical anisotropy of piezoelectric ceramics has been developed.

Effects of aspect ratio on the mode couplings of thin-film bulk acoustic wave resonators

We studied mode couplings in thin film bulk acoustic wave resonators of a piezoelectric film on a dielectric layer operating with the fundamental thickness-extensional mode. A system of plate equations derived in our previous paper was used which includes the couplings to the unwanted in-plane extension, flexure, fundamental and second-order thickness shear modes. It was shown that the couplings depend strongly on the plate length/thickness ratio. For a relatively clean operating mode with weak couplings to unwanted modes, a series of discrete values of the plate length/thickness ratio should be avoided and these values were determined in the present paper. The results can be of great significance to the design and optimization of film bulk acoustic wave resonators.

Characteristics of an AlN-based bulk acoustic wave resonator in the super high frequency range

We have evaluated the electrical performance of bulk acoustic wave (BAW) resonators in the range of resonance frequency from 5 to 20 GHz. The BAW resonators, consisting of a piezoelectric AlN film and top and bottom electrodes of Al/Ti films, were designed and prepared in the fundamental thickness-extensional mode. The value of effective coupling coefficient ( k eff 2 ) up to 6% and constant QF factors were achieved in these frequency ranges, which closely followed the theoretical calculation. It was found that AlN films were suitable for high frequency application because of their superior piezoelectricity even in the ultra thin region of 200 nm thickness.

Frequency spectra of resonant vibration in disk plates of PbTiO3 piezoelectric ceramics

The frequency spectra of resonant vibration in disk plates of PbTiO3 piezoelectric ceramics were observed for diameter to thickness ratio (r) of 5 to 30 near the fundamental thickness extensional mode. The observed spectra could be classified into three groups of thickness mode and two groups of radial mode. For comparison, theoretical spectra for isotropic disk plate were also calculated for various Poisson's ratios (σ) of disk material on the basis of Gazis and Mindlin's theory. The calculations showed that the theoretical radial mode spectra can be divided into a strongly σ-dependent group and a slightly dependent one, and also showed that the upper ends of terrace-type spectra appear as a straight line at the cutoff frequency in a large-r region and may be corresponded to the thickness extensional mode. In fact, the fitting of the upper-end spectra to the experimental thickness extensional mode by adjusting σ, gives not only qualitative agreement of all experimental spectra with the theoretical ones, but also the best quantitative agreement with the strongly σ-dependent theoretical spectra. Thus, all observed spectra can be predicted nearly completely from the theory of isotropic disk plate by selecting a suitable equivalent σ which is 0.18 for the present anisotropic disk.