Proximity effect model of ultra-narrow NbN strips

Proximity effect model of ultra-narrow NbN strips

I. Charaev1*, T. Silbernagel1, B. Bachowsky1, A. Kuzmin1, S. Doerner1, K. Ilin1, A. Semenov2, D. Roditchev3, D. Yu. Vodolazov4, and M. Siegel1 1Institute of Micro- und Nanoelectronic Systems, Karlsruhe Institute of Technology (KIT), Hertzstrasse 16, 76187 Karlsruhe, Germany 2Institute of Optical Systems, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany 3Institut des Nanosciences de Paris, Université Pierre et Marie Curie-Paris 6 and CNRS-UMR 7588, 4 place Jussieu, 75252 Paris, France 4Institute of Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia

We show that narrow superconducting strips in superconducting (S) and normal (N) states are universally described by the model presenting them as lateral NSN proximity systems in which the superconducting central band is sandwiched between damaged edge-bands with suppressed superconductivity. The width of the superconducting band was experimentally determined from the value of magnetic field at which the band transits from the Meissner state to the static vortex state. Systematic experimental study of 4.9 nm thick NbN strips with widths in the interval from 50 nm to 20 m, which are all smaller than the Pearl’s length, demonstrates gradual evolution of the temperature dependence of the critical current with the change of the strip width.
I. INTRODUCTION Superconductivity and geometrical effects in low- dimensional structures close to the mesoscopic and quantum limits, i.e. in structures where the thickness, width and length separately or together become comparable and smaller than the coherence length  and magnetic field penetration depth , are in focus of numerous theoretical and experimental works. This interest is stimulated by the fundamental importance of the problem itself as well as by the variety of applications of thin-film superconducting nanostructures.
Primarily, dimensionality of a superconducting film on a dielectric substrate decreases with the decrease of the film thickness d. Dependences of the critical temperature on the thickness of superconducting films were intensively studied both experimentally and theoretically. It has been observed that in Nb [1, 2], NbN [3, 4, 5], TaN [6], TiN [7], Pb [8], Bi [9], WSi [10] and other elementary and compound superconducting films critical temperatures decrease with the decrease in their thicknesses. It is well established that for films prepared by optimized technology and having thicknesses much larger than the coherence length the transition temperature TC is independent of the thickness and equals TC of corresponding bulk specimens. When the film thickness of a uniformly disordered superconductor decreases to a value in the range from 10 to 50 nm, TC of such film starts to decrease. When the thickness further decreases to d  10 nm, TC drops dramatically and at thicknesses less than 2  3 nm the film transits to the insulating state (the superconductor-insulator transition - SIT). The exact values of the thickness benchmarks specified above depend on the material of superconductor, film deposition technology, and specific conditions of the film growth (crystalline mismatch to substrate material, temperature, deposition rate, partial pressure of

• ilya.charaev@kit.edu working gases, etc.). In spite of these differences the TC(d)-dependences of uniformly disordered films far from SIT in most cases are well described by the intrinsic proximity effect [11, 12]. In the framework of this model a film on the substrate is considered as a superconducting layer sandwiched between two thin layers which are either normal or possess significantly suppressed superconductivity. One of these layers is located on the surface of the film while another builds the interface between the film and the substrate. Presence of such layers has been demonstrated for NbN films [3, 13] by means of transmission electron microscopy (TEM). Thicknesses of oxidized layers were found to agree well with the thicknesses estimated in the framework of the proximity effect model. Furthermore, for NbN and NbTiN films with thicknesses of a few  values [14, 15], it has been shown that protecting the film with appropriate buffers and protection layers results in an increase of the critical temperature.
  Secondarily, the dimensionality of a superconducting film can be reduced by patterning the film into narrow strips. In contrast to the thickness dependences, dependences of TC and other superconducting and normal state properties on the width W of the strip has not been studied systematically. One of the reasons is complexity of reproducible patterning of superconducting films into elements with dimensions comparable to the coherence length of the studied material

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