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

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.

💡 Research Summary

This work investigates the superconducting properties of niobium nitride (NbN) thin films fabricated by plasma‑enhanced atomic layer deposition (PE‑ALD) and compares them with conventional reactive magnetron sputtered NbN. The motivation is to obtain high kinetic inductance (L□) superconductors for compact, low‑noise cryoelectronic components such as superinductors, efficient filters, and parametric amplifiers. High kinetic inductance arises from a large normal‑state sheet resistance (R□) combined with a sizable superconducting gap (Δ), as expressed by L□ = h R□ / (2π² Δ).

NbN films with thicknesses ranging from 25 nm down to 4 nm were grown on thermally oxidized silicon and sapphire substrates using a TBTDEN niobium precursor at 380 °C. The ALD process yields a polycrystalline cubic σ‑NbN phase with an average grain size of about 10 nm for a 40 nm film, indicating a nanocrystalline, non‑epitaxial microstructure. As the thickness is reduced, the normal‑state sheet resistance rises dramatically (from ~80 Ω at 25 nm to ~1400 Ω at 4 nm) while the critical temperature Tc falls from ~14 K to ~9 K. Despite this, the ratio Δ/kBTc remains around 2.14, substantially larger than the BCS weak‑coupling value of 1.76, suggesting strong‑coupling superconductivity that is relatively insensitive to thickness.

To probe the spatial uniformity of the superconducting order parameter, the authors performed ultra‑high‑vacuum scanning tunneling microscopy and spectroscopy (STM/STS) at base temperatures of 1.5 K (25 nm film) and 1.2 K (5 nm and 4 nm films). Differential conductance spectra (dI/dV) were acquired with a lock‑in technique (819 Hz, 70 µV modulation) and fitted to the conventional BCS density‑of‑states expression, allowing extraction of Δ and an effective tip temperature Ttip. For the 25 nm film, averaging 50 spectra along a 70 nm line gave Δ = 2.11 meV and Ttip ≈ 3 K. For the ultrathin 5 nm and 4 nm films, 200 spectra were collected along a 424 nm diagonal; the fits yielded Δ = 2.02 meV (Ttip ≈ 1.73 K) and Δ = 1.59 meV (Ttip ≈ 2.27 K), respectively.

Crucially, each individual spectrum was fitted independently, producing histograms of Δ values. The 5 nm film exhibited a mean Δ̃ = 2.02 meV with a standard deviation σ = 0.04 meV, while the 4 nm film showed Δ̃ = 1.59 meV with σ = 0.05 meV. These correspond to relative variations of only 2–3 %, far smaller than the grain size (3–10 nm) and the measurement span (≈300 nm). The authors therefore conclude that the superconducting gap is remarkably homogeneous across the film surface, even when the film thickness approaches the critical thickness for the superconductor‑insulator transition (d_c ≈ 3 nm for the ALD films).

For comparison, sputtered NbN films of similar thickness display pronounced spatial inhomogeneities: nanoscale variations associated with grain boundaries and tens‑of‑nanometers variations linked to thickness fluctuations. Moreover, the sputtered films undergo the superconductor‑insulator transition at a lower thickness (d_c ≈ 2 nm) and retain higher Tc and Δ, but at the cost of larger Δ disorder.

Using the measured R□ and Δ values, the kinetic inductance L□ was calculated via Eq. (1). The 25 nm film shows L□ ≈ 8 pH, the 5 nm film ≈ 93 pH, and the 4 nm film ≈ 183 pH. These values fall well within the range required for superinductors (L□ ≳ 10 pH) and for protecting delicate quantum circuits from environmental noise.

The authors attribute the exceptional homogeneity to the layer‑by‑layer nature of ALD, which provides precise thickness control and yields small, uniformly distributed grains. The combination of high normal‑state resistance, large kinetic inductance, and nanoscale uniformity makes PE‑ALD NbN an attractive platform for a variety of superconducting devices, including nanowire single‑photon detectors (SNSPDs), coherent quantum phase‑slip elements, and kinetic‑inductance‑based resonators.

In summary, the study demonstrates that PE‑ALD can produce NbN films that, even at thicknesses near the superconductor‑insulator transition, maintain a spatially uniform superconducting gap while offering high kinetic inductance. This resolves a key challenge in the development of low‑loss, high‑impedance superconducting components for quantum technologies.