Study of microwave acoustic attenuation in a multifrequency bulk acoustic wave resonator based on a synthetic diamond single crystal

Acoustic attenuation in a multifrequency bulk acoustic wave resonator based on the synthetic diamond single crystal is investigated. The acoustic energy loss in a layered piezoelectric Al/AlN/Mo/(001) diamond structure is analyzed. The depth of a damaged surface layer with a thickness of 20–30 nm in diamond after abrasive finishing is estimated using high-energy electron backscattered diffraction and observation of Kikuchi lines. The estimation shows that the acoustic energy loss at a diamond substrate roughness of up to 20 nm, as well as acoustic loss in thin films, is lower than the bulk acoustic attenuation by an order of magnitude and is of no fundamental importance. However, the surface roughness of the piezoelectric AlN film can contribute comparably with the bulk attenuation in the substrate. It is demonstrated that the transition from the Akhiezer to Landau–Rumer regime in diamond occurs at a frequency of ~1 GHz and the phonon–phonon relaxation time is ~1.6 × 10–10 s. Calculation of acoustic attenuation showed that, although at a frequency of ~1 GHz the acoustic loss in diamond is somewhat higher than in well-known materials with a low attenuation level, the loss in diamond becomes noticeably lower as frequency increases to 8–10 GHz. The obtained maximum experimental value Qf ≈ 10 × 1013 Hz (9.5 GHz) makes synthetic diamond promising for microwave acoustoelectronic devices.