Nonequilibrium model of the superconducting tunneling junction x-ray detector

Giaever-type superconducting tunneling junctions are shown to be sensitive to the ionization energy of low-energy x-ray photons. The Mn Kα and Mn Kβ x-ray photons from a ${\mathrm{Fe}}^{55}$ source were detected with an energy resolution of 67 eV full width at half maximum (FWHM) at an energy of 5.89 keV with Sn/Sn oxide/Sn junctions evaporated on fused silica and operated at a temperature of 0.38 K. In this paper, a model of this detector is presented. The basic features are well described by dynamical Cooper-pair breaking and the relaxation mechanisms of nonequilibrium superconductivity. Quasiparticle diffusion had to be included in order to explain the observed data. The solutions of the four coupled Rothwarf-Taylor equations, one quasiparticle equation and one 2Δ-phonon equation for each of the two films, agree reasonably well with measured pulse shapes.