Spatial homogeneity of superconducting order parameter in NbN films grown by atomic layer deposition

TL;DR

The paper addresses whether NbN films grown by plasma-enhanced ALD (PE-ALD) maintain a spatially uniform superconducting order parameter $\Delta$ despite high normal-state resistance and proximity to the superconductor–insulator transition. It employs low-temperature scanning tunneling microscopy/spectroscopy to map local $dI/dV$ spectra and extract $\Delta$ via BCS fits across 25 nm, 5 nm, and 4 nm films, building histograms of $\Delta$ and assessing spatial variation. Key findings show mean $\Delta$ values of 2.11 meV (25 nm), 2.02 meV (5 nm), and 1.59–1.60 meV (4–5 nm) with a narrow dispersion ($\sigma \approx 0.04$–$0.05$ meV, i.e., 2–3%), and $\Delta/k_B T_c$ around $2.14 \pm 0.05$, higher than the BCS value of 1.76 for most films. The films reach sheet inductances up to $L_\square \approx 100$–$200$ pH with sheet resistances up to $R_\square \approx 1400$ Ω, indicating homogeneous superconducting behavior suitable for nanoscale devices such as SNSPDs and quantum circuits, and contrasting with more spatially inhomogeneous sputtered NbN at comparable thicknesses.

Abstract

Due to their high kinetic inductance, highly disordered superconducting thin films are a potential hardware for the realization of compact, low-noise elements in cryoelectronic applications. However, high disorder typically results in structural defects that cause spatial inhomogeneity of the superconducting order parameter, thereby impairing the film's properties. Here, we employ scanning tunneling microscopy to demonstrate that NbN thin films fabricated by plasma-enhanced atomic layer deposition (PE-ALD) exhibit unusual spatial homogeneity, even at thicknesses approaching the superconductor-insulator transition. Tunneling spectra acquired across the sample surface show only small variations of the order parameter with a standard deviation of 2-3%, on length scales that significantly exceed the film's grain size. At the same time, the films achieve a relatively high sheet resistance (up to 1400 Ohm) and, consequently, a high sheet kinetic inductance (up to approximately 200 pH), making them well-suited for applications.

Figures (4)

• Figure 1: Critical temperature of NbN grown by PE-ALD on silicon substrates as a function of the film thickness. The colored triangles mark the data points of the 4 nm, 5 nm and 25 nm films investigated in this study.
• Figure 2: LT-STM analysis of a 25 nm NbN film on silicon. (a) STM topography and (b) normalized tunneling spectrum averaged over 50 spectra taken along a 70 nm line. The shown BCS fit (Eq. \ref{['didv_fit']} and \ref{['bcs_dos']}) yields an order parameter $\Delta=2.11\rm\,meV$ and an effective tip temperature $T_\mathrm{tip}=3.03\rm\,K$.
• Figure 3: LT-STM analysis of a 5 nm NbN film on sapphire and a 4 nm NbN film on silicon. (a) STM topography and (b) normalized tunneling spectrum averaged over 200 spectra taken along a 424 nm line for each of the two films. The shown BCS fits yield order parameters $\Delta=2.02\rm\,meV$ and $1.60\rm\,meV$ and effective tip temperatures $T_\mathrm{tip}=1.73\rm\,K$ and $2.27\rm\,K$ for the 5 nm and 4 nm film, respectively.
• Figure 4: Spatial homogeneity of the superconducting order parameter. (a) Waterfall plot of the 200 tunneling spectra measured along a 424 nm line across the 5 nm NbN film on sapphire and 4 nm NbN film on silicon. Spectra are offset for visual clarity. (b) Histogram of the order parameters for both films obtained by BCS fits to each of the individual spectra shown in (a). The mean value $\tilde{\Delta}$ and the standard deviation $\sigma$ of a Gaussian fit (Eq. \ref{['gaussian_fit']}) are indicated.