Dynamics of nonequilibrium quasiparticles in narrow-gap superconducting tunnel junctions

Abstract

The latest generation of high quality, narrow gap, superconducting tunnel junctions ͑STJs͒ exhibits a steadystate and time-dependent behavior which cannot be described satisfactorily by previous treatments of nonequilibrium quasiparticle ͑qp͒ dynamics. These effects are particularly evident in experiments using STJs as detectors of photons, over the range from near infrared to x ray. In this paper, we present a detailed theoretical analysis of the spectral and temporal evolution of the nonequilibrium qp and phonon distributions in such STJs excited by single photons, over a wide range of excitation energy, bias voltage, and temperature. By solving the coupled set of kinetic equations describing the interacting excitations, we show that the nonequilibrium qp distribution created by the initial photoabsorption does not decay directly back to the initial undisturbed state in thermal equilibrium. Instead, it undergoes a rapid adiabatic relaxation to a long-lived, excited state, the spectral distribution of which is nonthermal, maintained by a balance between qp creation, recombination, and trapping. The model is able to describe successfully photoabsorption data taken on several different aluminum STJs, using a single set of parameters. Of particular note is the conclusion that the local traps responsible for qp loss are situated specifically in the region of Nb contacts.

Inelastic scattering of quasiparticles in a superconductor with magnetic impurities

“…The smaller exponent for QP trapping on a discrete state has an important implication for nonequilibrium effects in multiple tunneling superconducting tunnel junctions ͑STJs͒. 16,17 In order to estimate the order of magnitude of the continuum-bound trapping rate, we consider Ta as a typical superconductor. Assuming the presence of Kondo impurities with a discrete state residing deep inside the gap, we will take for an estimate ⑀ 0 =1/ 2⌬.…”

“…However, the decrease in pair-breaking efficiency for sub-2⌬ phonons may be partially compensated by their longer escape time, which occurs because phonons escape from an acoustically softer superconductor into a rigid dielectric substrate is constrained to lie within the critical escape cone defined by the critical incidence angle for the superconductor-substrate interface. 16 Thus the process of phonon scattering from outside to inside the critical cone becomes crucial; in general, this conversion is less efficient for lower-energy phonons. Nevertheless despite the extra complications discussed above, impurity enhanced recombination is the principal recombination channel at the lowest temperatures because of the much higher occupation numbers for the impurity bound states.…”

Energy Down-Conversion and Thermalization in Metal Absorbers

“…Finally localized microscopic states associated with magnetic moments, either in the bulk or at the surface, are known to exist inside the gap region [33]. Modelling of STJ responsivity and signal decay time as a function of temperature and photon energy made it possible to determine local trap densities and their levels [20,27] (Figs. 6 and 7) give typical results.…”

Experimental and theoretical response of distributed read-out imaging devices with imperfect charge confinement

“…Previous results 15 on STJs have indicated that quasiparticle losses inside the STJ are due to bulk material losses and a concentration of loss centers near the leads, especially the plugs which are made of higher gap material to avoid outdiffusion of quasiparticles. Recent developments have indicated that quasiparticle losses in superconducting materials may be due to a very small amount of magnetic impurities in the high grade superconducting material.…”

“…This process, denoted by the relaxation rate ␥ s ͑i͒ , depends on the STJ proximisation and can be calculated. 15 Due to sequential tunnelling quasiparticles gain energy, equal to twice the applied bias voltage ͑2 eV b ͒ with each tunnelling cycle, and after a sufficient number of cycles without relaxation the quasiparticles are promoted from group 3 into group 2. The number of tunnels needed to reach an energy above the energy gap of the absorber and thus to change the trapping efficiency can be adjusted for a given STJ lay-out with the bias voltage.…”