The temperature dependence of the superconducting density {nₒ} { ^{ - 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 { ₀}/{k₁}{T₂} = 2. 5 describes well the low-temperature part of the dependence ~{nₒ}, but deviates from the experimental results near the superconducting transition {T₂}. 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 nₒ^{2{D}} (T 0) = 3. 2 {10^{13}}~\, \, c{{m}^{ - 2}}. The applied method can be used to characterize the inhomogeneity of grown thin films.
Nikolaev et al. (Sun,) studied this question.