Modeling the power flow in normal conductor-insulator-superconductor junctions

Abstract

Normal conductor-insulator-superconductor ͑NIS͒ junctions promise to be interesting for x-ray and phonon sensing applications, in particular due to the expected self-cooling of the N electrode by the tunneling current. Such cooling would enable the operation of the active element of the sensor below the cryostat temperature and at a correspondingly higher sensitivity. It would also allow the use of NIS junctions as microcoolers. At present, this cooling has not been realized in large area junctions ͑suitable for a number of detector applications͒. In this article, we discuss a detailed modeling of the heat flow in such junctions; we show how the heat flow into the normal electrode by quasiparticle back-tunneling and phonon absorption from quasiparticle pair recombination can overcompensate the cooling power. This provides a microscopic explanation of the self-heating effects we observe in our large area NIS junctions. The model suggests a number of possible solutions.

Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

“…The problem intrinsic to junctions with large overlap ͑especially at the lowest temperatures͒ stems from the larger density of quasiparticles present in the superconductor, due to the fact that quasiparticles require a larger time to exit the junction region and escape from the superconductor. Therefore this excess of quasiparticles in general alters the refrigerator performance by returning energy to the normal electrode, mainly due to back tunneling from the superconductor as well as due to recombination processes in which phonons can enter and heat up the N region ͑Kaplan et al., 1976;Jochum et al, 1998;Ullom and Fisher, 2000͒. In addition, inelastic scattering with phonons and dynamic impurities can also lead to an excess of quasiparticles.…”

Etching suspended superconducting tunnel junctions from a multilayer

“…The discrepancy with the estimation of the total heat load is presumably due to the overheating of the superconducting electrodes submitted to a large quasi-particle current. 9,10,14 This effect actually shows up experimentally as a slight back-bending feature on the current-voltage characteristic close to the gap edge. The related superconductor temperature T s can be estimated by using it as a free parameter in Eq.…”

“…9 The same current is also expected to heat the superconductor in the vicinity of the junctions area. 10 Eventually, for a given cooling power, an efficient electronic cooling relies on a thermal decoupling of cooled electrons and phonons from the environment, including the substrate. It is thus highly desirable to suspend the cooled normal metal over the substrate.…”

High-power on-chip microrefrigerator based on a normal- metal/insulator/superconductor tunnel junction

“…The third term accounts for power flow from backtunneling of quasiparticles in the superconducting electrode and absorption of phonons emitted by quasiparticle recombination. 9 We make the simplifying assumption that power loading from these two effects is equal to ␤ P s , where ␤Ͻ1 is a parameter dependent only on T b , and P s ϭIVϩP n is the net power dissipated in the superconducting electrode. The last term in Eq.…”

“…The latter can be accomplished by a combination of a thinner SiN membrane and various surface treatments. 12,14 Low values of ␤ can be realized by using along mean-free-path superconductor to maximize the diffusion length and reduce the quasiparticle density, 9,13 and by utilizing smaller area tunnel junctions. …”