Peculiarities of energy trapping of the UHF elastic waves in diamond-based piezoelectric layered structure. II. Lateral energy flow.

Features of an acoustic energy trapping and outflow in a High-overtone Bulk Acoustic Resonator (HBAR) were considered. On the example of a specified resonator based on a piezoelectric layered structure (PLS) as "Al/AlN/Mo/(100) diamond", the simulation of the propagation of microwave acoustic waves in the range of 10-6000 MHz by Finite Element Method (FEM) in COMSOL Multiphysics has been carried out. It was found that the magnitude of acoustic energy retained in the substrate under the bottom electrode depends substantially on the relation between the HBAR's antiresonance frequency fa,n and the cut-off frequencies fs,n-k and fs,n-k+1 of the substrate. The term "cut-off frequency" has the meaning of the frequency point when integer value of half-waves fits along the thickness of substrate. Parameter gk,n estimating the degree of the HBAR's energy trapping has been proposed. If 0.5 < gk,n < 1, then a retention of acoustic energy in the HBAR's center as a maximal ET-effect at the overtone frequency fa,n should be fulfilled. Increasing the width of the top electrode as well as the HBAR's aperture should expand the frequency interval in which the retained elastic energy in the vicinity of the HBAR's center will be greater than the similar outside. It was shown that the area-averaged Umov-Poynting's power energy flow vector from the HBAR's center in the lateral directions increases when approaching the Thin Film Piezoelectric Transducer half-wave resonance frequency from below, and then decreases sharply in the point of complete energy trapping. This can be explained by the outflow of acoustic wave energy from the center to the periphery as a consequence of the transformation of an operational longitudinal acoustic mode into waves of Lamb type mainly. Results on the peculiarities of an energy trapping effect will be useful developing the HBARs and HBAR-based acoustic sensors operating at microwave frequencies.

Peculiarities of energy trapping of the UHF elastic waves in diamond-based piezoelectric layered structure. I. Waveguide criterion.

Finite Element Modeling of the peculiarities of the trapping energy phenomenon in application to the piezoelectric layered structure (PLS) "Al/(0 0 1) AlN/Mo/(1 0 0) diamond" has been fulfilled. The resonant properties of longitudinal bulk acoustic waves (BAW) as well as frequency dependence of impedance within the 1 - 6 GHz band have been studied. The investigation of distribution of elastic energy flow and elastic displacements in a PLS cross-section allowed us to obtain an important information on energy trapping (ET) in PLS. Experimentally and as a result of modeling, it has been found that Q minimums are observed in PLS at quarter-wave resonance in the thin-film piezoelectric transducer (TFPT). Maximal Q value was observed at half-wave resonance in TFPT. It has been established that the ET-effect depends considerably on the mutual location of the n-th overtone's antiresonant frequency fa,n and cut-off frequencies of substrate fs,n-k-1 and fs,n-k where fs,n-k-1fs,n-k, when the BAW energy excites the symmetrical or antisymmetrical Lamb waves.

Excitation of hypersonic acoustic waves in diamond-based piezoelectric layered structure on the microwave frequencies up to 20GHz.

First ultrahigh frequency (UHF) investigation of quality factor Q for the piezoelectric layered structure «Al/(001)AlN/Mo/(100) diamond¼ has been executed in a broad frequency band from 1 up to 20GHz. The record-breaking Q·f quality parameter up to 2.7·1014Hz has been obtained close to 20GHz. Frequency dependence of the form factor m correlated with quality factor has been analyzed by means of computer simulation, and non-monotonic frequency dependence can be explained by proper features of thin-film piezoelectric transducer (TFPT). Excluding the minimal Q magnitudes measured at the frequency points associated with minimal TFPT effectiveness, one can prove a rule of Qf∼f observed for diamond on the frequencies above 1GHz and defined by Landau-Rumer's acoustic attenuation mechanism. Synthetic IIa-type diamond single crystal as a substrate material for High-overtone Bulk Acoustic Resonator (HBAR) possesses some excellent acoustic properties in a wide microwave band and can be successfully applied for design of acoustoelectronic devices, especially the ones operating at a far UHF band.