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

Abstract

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.