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Epitaxial niobium-nitride thin films with a critical temperature of Tc=16Kand a thickness of 100nm were fabricated on MgO(100) substrates by pulsed laserdeposition. Low-temperature magnetic force microscopy (MFM) images of thesupercurrent vortices were measured after field cooling in a magnetic field of3mT at various temperatures. Temperature dependence of the penetration depthhas been evaluated by a two-dimensional fitting of the vortex profiles in themonopole-monopole model. Its subsequent fit to a single s-wave gap functionresults in the superconducting gap amplitude Delta(0) = 2.9 meV = 2.1*kB*Tc, inperfect agreement with previous reports. The pinning force has beenindependently estimated from local depinning of individual vortices by lateralforces exerted by the MFM tip and from transport measurements. A goodquantitative agreement between the two techniques shows that for low fields, B<< Hc2, MFM is a powerful and reliable technique to probe the local variationsof the pinning landscape. We also demonstrate that the monopole model can besuccessfully applied even for thin films with a thickness comparable to thepenetration depth.

physical review. b, condensed matter and materials physics

Quantitative assessment of pinning forces and the superconducting gap in  NbN thin films from complementary magnetic force microscopy and transport  measurements