Contactless Measurement of the Superconducting Density in a Thin Niobium Nitride Film

The temperature dependence of the superconducting density n_s~ λ ^ - 2~ of a niobium nitride (NbN) film with a thickness d = 8 nm was measured using a contactless technique based on analyzing the mutual inductance of two coils with the sample placed between them. The Bardeen–Cooper–Schrieffer (BCS) theory with a correction Δ ₀/k_BT_c = 2.5 describes well the low-temperature part of the dependence ~n_s, but deviates from the experimental results near the superconducting transition T_c. The best agreement with the experiment was obtained by taking into account the Berezinskii–Kosterlitz–Thouless (BKT) transition smoothed by inhomogeneities of the system. As a result, the superconducting density was numerically estimated at n_s^2D( T → 0 ) = 3.2 × 10^13~\,\,cm^ - 2. The applied method can be used to characterize the inhomogeneity of grown thin films.