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Japanese Journal of Applied Physics

Evaluation of Attenuation Constants of Superconducting NbN Coplanar Waveguides

Hirotake Yamamori, Akira Shoji

Published Jul 1, 2005• 1 citation
Publisher

Abstract

Attenuation constants of superconducting NbN coplanar waveguides (CPWs) have been evaluated by measuring their transmission coefficients and reflection coefficients with a network analyzer. It has been found that the attenuation constant of NbN CPWs rapidly increases when their thicknesses are reduced below the penetration depth (300 nm). It has also been found that the experimentally measured attenuation constants of NbN CPWs coincide well with the numerically calculated ones.

DOI
10.1143/jjap.44.l961

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Attenuation constants of superconducting NbN coplanar waveguides (CPWs) have been evaluated by measuring their transmission coefficients and reflection coefficients with a network analyzer. It has been found that the attenuation constant of NbN CPWs rapidly increases when their thicknesses are reduced below the penetration depth (300 nm). It has also been found that the experimentally measured attenuation constants of NbN CPWs coincide well with the numerically calculated ones.
An analytical expression for the kinetic inductance of the superconducting coplanar waveguide is given using the conformal mapping technique. This expression is shown to be in good agreement with experimental results obtained from the temperature dependence of the resonant frequency of the NbN coplanar waveguide resonators, especially in the case of a film thickness smaller than the magnetic penetration depth. It is also shown that the magnetic penetration depth of the superconducting thin films can be evaluated by this method.
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The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide resonator consisting of a current-carrying central conductor, adjacent slots, and ground planes that return the current. The analysis focuses on films of thickness d obeying d<2λ (λ is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length Λ=2λ2/d. Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small Λ. Exact results for arbitrary Λ are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.