Properties of Substrate Phonon Events in Superconducting Tunnel Junctions Induced by X-Ray Absorption

The spectra of substrate phonon events induced by illuminating with X-rays obtained with Nb-based superconducting tunnel junctions (STJs) fabricated on a sapphire substrate were examined. We constructed a geometrical model in which the collection efficiency of phonons is proportional to the solid angle subtended to the STJ from the position of the absorption. By using the Monte-Carlo simulation, we succeeded in fairly reproducing the features of the spectra obtained by our measurements. A comparison of the model spectra with the measured ones revealed that a mismatch of the acoustic impedance at the junction-substrate interface and the spatial spread of a phonon cloud play an important role in the determination of the spectra. By including these effects, we show that the measured spectra can be well reproduced by adjusting only one free parameter, the radius of the phonon cloud. We estimated this radius in a sapphire substrate to be ∼20 µm under 5.9 keV X-ray illumination.