Lateral phonon propagation between superconducting devices on a Si/SiO2 substrate

The propagation of acoustic phonons between mesoscopic superconducting devices on a Si substrate with a SiO2 surface layer was studied in terms of emission-detection measurements of phonons of an energy approximately 350μeV. The emitter and detector of the phonons were composed of mesoscopic Al/AlOx/Al junctions, and the recombination phonons in the Al electrode were used for propagation measurement. It was observed that the phonons propagated laterally from the emitter to the detector as well as the vertical propagation into the interior of the substrate. The results of a comparative measurement using a device with an etched groove in the SiO2 layer between the emitter and the detector indicate that the lateral propagation path to the detector is almost completely through the SiO2 surface layer (>97%), and the propagation fashion is leaky two-dimensional propagation with the leakage due to their transmission across the SiO2–Si interface to the Si substrate. A leaky decay factor F(d) for the lateral propagation was experimentally derived as a function of the distance d between the emitter and the detector, and a simple model for F(d) was formulated on the basis of the acoustic mismatch model of phonon transmission across the interface. The devised model well explained the observed behavior of F(d). The model also indicates that the lateral propagation of phonons is mostly induced by those emitted from the emitter at nearly the critical angle for perfect reflection at the SiO2–Si interface.