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. 2022 Nov 22;12(23):4109. doi: 10.3390/nano12234109

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© 2022 by the authors.

Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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Current density as a function of the temperature, normalized to $T_{c}$ , for the whole set of NbN films deposited on the Al $_{2}$ O $_{3}$ r-cut substrate. Lines are the result of the least-squares fitting by the Ginzburg–Landau equation (see ref. [31]). Inset: thickness dependence of the critical current density at zero temperature, $J_{c 0}$ , for NbN films deposited on Al $_{2}$ O $_{3}$ r-cut (circles), Al $_{2}$ O $_{3}$ c-cut (triangles), MgO (stars), SiO $_{2}$ (square).