The response of superconducting pair-breaking detectors is dependent on the details of the quasiparticle distribution. In Kinetic Inductance Detectors (KIDs), where both pair breaking and non-pair breaking photons are absorbed simultaneously, calcula
ting the detector response therefore requires knowledge of the often nonequilibrium distributions. The quasiparticle effective temperature provides a good approximation to these nonequilibrium distributions. We compare an analytical expression relating absorbed power and the quasiparticle effective temperature in superconducting thin films to full solutions for the nonequilibrium distributions, and find good agreement for a range of materials, absorbed powers, photon frequencies and temperatures typical of KIDs. This analytical expression allows inclusion of nonequilibrium effects in device models without solving for the detailed distributions. We also show our calculations of the frequency dependence of the detector response are in agreement with recent experimental measurements of the response of Ta KIDs at THz frequencies.
We calculate nonequilibrium quasiparticle and phonon distributions for a number of widely-used low transition temperature thin-film superconductors under constant, uniform illumination by sub-gap probe and pair-breaking signal photons simultaneously.
From these distributions we calculate material-characteristic parameters that allow rapid evaluation of an effective quasiparticle temperature using a simple analytical expression, for all materials studied (Mo, Al, Ta, Nb, and NbN) for all photon energies. We also explore the temperature and energy-dependence of the low-energy quasiparticle generation efficiency $eta$ by pair-breaking signal photons finding $eta approx 0.6$ in the limit of thick films at low bath temperatures that is material-independent. Taking the energy distribution of excess quasiparticles into account, we find $eta to 1$ as the bath temperature approaches the transition temperature in agreement with the assumption of the two-temperature model of the nonequilibrium response that is appropriate in that regime. The behaviour of $eta$ with signal frequency scaled by the superconducting energy gap is also shown to be material-independent, and is in qualitative agreement with recent experimental results. An enhancement of $eta$ in the presence of sub-gap (probe) photons is shown to be most significant at signal frequencies near the superconducting gap frequency and arises due to multiple photon absorption events that increase the average energy of excess quasiparticles above that in the absence of the probe.
