Quasiparticle diffusion, edge losses, and back-tunneling in superconducting tunnel junctions under x-ray irradiation

The efficiency of the charge collecting mechanism of a radiation detector based on superconducting tunnel junctions depends strongly on the competition between tunneling and losses of quasiparticles in the electrodes of the junction. In this article we discuss the loss of quasiparticles, both in the bulk and at the edges of the electrodes. The quasiparticle loss taking place during their diffusion in the junction limits the amount of charge carriers tunneling and thereby the energy resolution of the detector. A charge amplification process caused by multiple tunneling of quasiparticles is beneficial to higher signal to noise ratios. Such multiple tunneling is always present in the case of junctions based on symmetrical electrodes. In this article we present a theory for the detector response which takes into account both multiple tunneling and the diffusion of quasiparticles. A model is presented for the spectral response of the detector based on four parameters one of which is the degree of back-tunneling present in the device. Analytical solutions of the model for rectangular and circular junctions are discussed. The predictions of the theory are compared with an experimental pulse height spectrum obtained on a ${\mathrm{Nb/Al}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{3}}\mathrm{/Nb}$ junction.