Effect of oxygen plasma treatment on the structural and superconducting properties of atomic-layer-deposited NbN thin films

Introduction

Ultrathin NbN films combine superconductivity at liquid-helium temperature with a short coherence length and a high normal-state resistivity. They remain superconducting down to thicknesses of a few nanometers, which suits them to nanoscale patterning and to large kinetic inductance. Films with thicknesses of a few nanometers form the active layer of superconducting nanowire single-photon detectors (SNSPDs) ¹, hot-electron bolometer mixers ², and high-kinetic-inductance circuit elements ³. In addition, all-nitride qubit circuits employ NbN for junctions and wiring, motivated by its chemical stability against oxidation ⁴. NbN interconnects with high kinetic inductance have also been integrated with aluminum Josephson junctions in a hybrid technology for quantum devices ⁵. Plasma-enhanced atomic layer deposition (PE-ALD) provides NbN films for such devices with monolayer thickness control and wafer-scale homogeneity ⁶. At these thicknesses the device performance follows the film properties directly.

Oxygen affects these films at every stage of their life. Air exposure forms a native oxide of 0.5 to 1 nm on NbN within minutes ⁷, following the oxidation pathway to $\mathrm{Nb}_2\mathrm{O}_5$ above an intermediate niobium oxynitride [^11, ^12]. The sheet resistance of 5 nm NbN films can rise by over 40% after two years in atmosphere ⁸. In sputtered NbN, oxygen can moreover penetrate deep into the film along the grain boundaries and degrade the superconductivity of the bulk ⁹, and 3 nm NbTiN films show no superconducting transition down to 3 K unless the surface is passivated ¹⁰. On the microwave side, the amorphous pentoxide is a dielectric that hosts two-level systems, which limit the quality factor of resonators and the coherence time of qubits ¹¹, and surface oxidation could shift the operating frequency of kinetic-inductance circuits ¹². At the same time, $\mathrm{O}_2$ plasma is deliberately applied to NbN during nanofabrication, for resist stripping and most recently as the oxidation half-cycle of atomic layer etching ¹³.

These observations/studies leave open where the oxygen acts on the film. Oxygen confined to a surface oxide reduces the superconducting cross section, whereas oxygen entering the grain boundaries or the lattice acts as bulk disorder and suppresses the critical temperature [^14, ^21, ^22]. Which case applies evidently depends on the microstructure of the film, and for PE-ALD NbN it has not been established. Natural aging is unsuited to answer this, since it is slow, poorly reproducible, and convolves oxidation with other degradation mechanisms. A controlled $\mathrm{O}_2$ plasma dose separates the oxidation from these variables and accelerates it to practical timescales, so that the treated films serve as a proxy for aged films. If the oxide growth is self-limiting, the same treatment could moreover serve as a deliberate passivation of the surface, since the terminal oxide leaves nothing to oxidize further. The temperature-dependent switching current of a nanowire then distinguishes the two cases, since its low-temperature value probes the condensate while its behavior near $T_{\mathrm{c}}$ responds to perturbations on the scale of the diverging coherence length.

In this work, we establish a controlled oxygen incorporation in PE-ALD NbN films with a nominal thickness of 10 nm (11.4 nm by x-ray reflectivity, XRR) by O$_2$ plasma exposure, which grows a surface oxide without material removal, and determine its effect on the structural and superconducting transport properties. Films exposed for 0 to 60 s are characterized by grazing-incidence x-ray diffraction (GIXRD) and x-ray photoelectron spectroscopy (XPS) before and after sputtering and by $R(T)$ and switching-current measurements on 500 nm wide nanowires patterned from them. Those results will be compared with XRR and spectroscopic ellipsometry from colleagues on the same samples [23]. We find that the plasma oxidizes the film surface to Nb$_2$O$_5$ in a self-limiting way while the bulk of the film remains unchanged, so that it could be used as passivation. The critical temperature shows no degradation, and the switching current at 4.2 K is nearly the same for all samples except B_20s. The oxygen signature is confined to temperatures near $T_{\mathrm{c}}$, consistent with a weakened surface layer acting by the proximity effect [24]. At these doses the oxygen therefore narrows the temperature range of the supercurrent but does not systematically reduce the low-temperature current-carrying capacity of the wires.

Experimental Methods

Film deposition and plasma treatment

Four 10 $\times$ 10 mm$^2$ chips were diced from a commercially available 100-mm boron-doped silicon wafer. On these substrates a 4 nm Al$_2$O$_3$ buffer layer was deposited by atomic layer deposition (ALD) in an Oxford OpAL reactor. This layer serves as an etch-stop during the subsequent patterning of the NbN. On top of this substrate, a 10 nm NbN film was grown by PE-ALD [6]. The reactor was operated at 5–300 mTorr with a substrate table temperature of 380 °C. The setup is installed inside a nitrogen-filled custom glovebox, which reduces oxygen contamination in the reactor during sample handling and processing. Each deposition cycle consisted of four steps. First, the substrate was exposed to the metal-organic precursor (tert-butylimido)tris(diethylamino)niobium (TBTDEN) for 4 s to form an adsorbed monolayer. The chamber was then purged with argon to remove excess precursor. In the third step, a remote hydrogen plasma of 300 W was applied for 60 s to reduce and nitridize the adsorbed monolayer, followed by a final argon purge. The number of cycles was set to 188 to reach the target thickness of 10 nm. The growth per cycle was 0.532 Å.

For the controlled incorporation of oxygen, three of the four samples were exposed to an O$_2$ plasma in a SENTECH Instruments GmbH SI 500-408 reactive ion etching (RIE) system with a capacitively coupled plasma source. The process parameters were 4 sccm O$_2$ flow, 6 Pa chamber pressure, and 50 W rf power. Plasma exposure times of 20, 40, and 60 s were applied, resulting in the samples B_20s, C_40s, and D_60s, respectively. The as-deposited sample, which was not exposed to oxygen, is labeled A_0s. For the XPS analysis, a duplicate pair of samples was prepared with the same number of ALD cycles and the same plasma process at the two exposures of 0 and 60 s. This pair was grown on HF-cleaned Si substrates without the Al$_2$O$_3$ buffer layer to exclude substrate-related interference in the compositional analysis and was not patterned into wires. After the plasma treatment, the unpatterned films were characterized as described in Sec. II B. Subsequently, the samples were coated with AR-P 6200.04 electron-beam resist (Allresist GmbH) and patterned by electron-beam lithography (EBL) using a Vistec SB350-OS system. The structures were transferred into the NbN film by RIE with 40 sccm CF$_4$ at 100 W and 9 Pa, carried out in the same RIE chamber used for the O$_2$ plasma treatment after a machine preconditioning step. The etch endpoint was monitored by in situ reflectometry. The etch was stopped manually when the reflection signal changed from the NbN film to the substrate. The resulting etch times were 49, 80, 72, and 70 s for A_0s to D_60s. The lithographic layout contained four-point measurement structures with a width of 500 nm at a width-to-length ratio of 1:10.

Characterization techniques

Structural and compositional analysis

GIXRD measurements were performed on the unpatterned films using a PANalytical X’Pert PRO diffractometer with a Cu K$\alpha$ source ($\lambda= 1.5406$ Å). The GIXRD patterns were recorded at a fixed incidence angle of $\omega= 2^\circ$ as a $2\theta$ scan from 10° to 90°, repeated 45 times for statistics, to identify the crystalline phases and to evaluate the texture. Crystallite sizes were determined from a line-profile analysis of the (111) reflection using a Williamson-Hall approach in size-only mode. XPS was carried out with a PHOIBOS 150 hemispherical analyzer and monochromated Al K$\alpha$ radiation ($h\nu= 1486.7$ eV) from a FOCUS 500 monochromator with an XR50M X-ray source (SPECS Surface Nano Analysis GmbH). Survey and high-resolution core-level spectra (Nb 3d, N 1s, O 1s, C 1s) were recorded in the as-received state and after 15 min of Ar$^+$ sputtering (700 V, approximately 4 μA/cm$^2$ at $5 \times10^{-5}$ mbar) to distinguish surface contamination from the composition at the center of the film. The film thicknesses were determined by XRR and spectroscopic ellipsometry was performed on the same unpatterned films to extract the Drude transport parameters (carrier density, mobility, and scattering time). The XRR analysis, the optical modeling and fitting procedure are described in detail in Ref. [23].

Electrical transport and critical current

Resistance-temperature $R(T)$ curves were recorded in a four-point geometry on the patterned 500-nm-wide nanowire structures using a Keithley 2450 source-measure unit with a bias current of 300 nA. The critical temperature $T_{\mathrm{c}}$ was defined as the midpoint of the resistive transition (50% of $R_{\max}$), and the transition width $\Delta T_{\mathrm{c}}$ as the temperature interval between the 90% and 10% resistance points. The measurement setup determines $T_{\mathrm{c}}$ with an accuracy of approximately 0.01 K. Temperature-dependent critical current measurements were performed on the same 500-nm-wide, 5-µm-long nanowire bridges from 4 K to 13 K in 0.25 K steps. The sample was mounted on a custom dipstick immersed in liquid helium. A resistive heater was installed on the underside of the sample breadboard to allow controlled warming above the helium bath temperature of 4.2 K. The heater was mounted such that it is additionally coupled to the sample through the back side by a screw, which tightly connects both in a thermally conducting way. The temperature was set and stabilized with a Lakeshore 336 temperature controller before each measurement point. At each stabilized temperature, the critical current was determined from current-voltage ($I$-$V$) characteristics acquired with the Keithley 2450. The bias current was swept from 0 to 400 µA and back to 0 in 10 nA steps. The switching current $I_{\mathrm{sw}}$ was defined as the bias current at which the nanowire undergoes a sudden transition from the superconducting zero-resistance state to the normal-conducting (resistive) state on the forward sweep. The retrapping current $I_{\mathrm{r}}$ was defined as the current at which the nanowire returns from the resistive state back to the superconducting state on the reverse sweep. Two consecutive sweeps were recorded at each temperature to assess the reproducibility of the measurement.

Results

Material characterization

GIXRD analysis

To evaluate the structural response to the plasma treatment, the four samples exposed for 0, 20, 40, and 60 s were characterized by GIXRD. The GIXRD patterns of all four samples [Fig. 1] confirm the formation

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of polycrystalline $\delta$-NbN (cubic) [7, 9], with diffraction peaks corresponding to the (111), (020), (022), and (131) planes. The (111) reflection is the most intense one, indicating a preferred orientation along the close-packed direction of the cubic lattice. No additional diffraction peaks or peak splitting are observed across the three O$_2$ plasma exposure conditions. This indicates that the $\delta$-NbN phase is preserved and that no secondary phase crystallizes upon the plasma treatment. The crystallite size from the Williamson-Hall analysis remains approximately 6.5, 7.0, and 6.5 nm for A_0s, B_20s, and C_40s, respectively, and decreases to 5.5 nm for D_60s. The microstrain term was set to zero because the microstrain uncertainties were found to be of the same order as the microstrain values themselves, rendering the combined size-plus-strain decomposition unreliable for these ultrathin films. The film thickness measured by XRR is 11.4, 11.8, 12.8, and 12.9 nm from A_0s to D_60s [23]. It is nearly the same for the two longest exposures. This suggests that the growth of the surface layer saturates between 40 and 60 s.

XPS analysis

XPS was performed on the A_0s and D_60s samples to determine the chemical composition at the two limiting O$_2$ plasma exposures. The spectra were recorded on the duplicate, unpatterned sample pair described in Sec. II A. Each sample was measured in the as-received state, which reflects the film surface (surface analysis), and after 15 min of Ar$^{+}$ sputtering, which removes approximately 5 nm and exposes the bulk (*center-of-film analysis). The background-subtracted core-level spectra are presented in Figure 2, with the surface analysis in the top row [Figure 2(a)–(Figure 2d)] and the center-of-film analysis in the bottom row [Figure 2(e)–(Figure 2h)].

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Ar⁺ bombardment of nitrides and oxides can introduce artifacts, including preferential sputtering of the lighter elements and ion-induced chemical reduction of surface oxides [12, 26]. Thus, the sputtered spectra reflect the composition at the center of the film only approximately. Since both samples were sputtered under identical conditions, relative comparisons between A_0s and D_60s remain valid.

a. Nb 3d core-level spectra The Nb 3d region contains contributions from four niobium bonding environments, identified by their relative positions [11] with the Nb–N 3d₅/₂ line observed at 204.1 eV as reference and a spin-orbit splitting of 2.7 eV [27]: Nb–N (3d₃/₂ at 206.8 eV), Nb–C at 204.6 eV (207.3 eV), the niobium oxynitride Nb₂N₂₋ᵧO₃₊ᵧ at 207.4 eV (210.1 eV), and Nb₂O₅ at 208.0 eV (210.7 eV). In the as-received state [Figure 2(a)], the Nb–N doublet is present in both samples and is more pronounced for A_0s. The Nb–C contribution lies within the Nb–N peak. The peak of A_0s at 207 eV is a superposition of the 3d₅/₂ line of the niobium oxynitride with the 3d₃/₂ lines of Nb–N and Nb–C.

For D_60s, the dominant peak at 208.15 eV corresponds to the 3d₅/₂ line of Nb₂O₅, a shoulder near 207 eV to the niobium oxynitride superposed with the 3d₃/₂ lines of Nb–N and Nb–C, and the peak at 210.9 eV mainly to the 3d₃/₂ line of Nb₂O₅ with a minor niobium oxynitride contribution. This indicates that the surface of A_0s consists of NbN with some NbC and a niobium oxynitride layer without a resolved Nb₂O₅ component, whereas the surface of D_60s is dominated by Nb₂O₅ with reduced NbN and minor NbC and niobium oxynitride contributions.

After sputtering [Figure 2(e)], both samples show the Nb–N doublet at 204.1 eV as the dominant contribution, accompanied by Nb–C, and a peak at 207 eV formed by the niobium oxynitride together with the 3d₃/₂ lines of Nb–N and Nb–C. No Nb₂O₅ component is resolved in the interior of either sample. The spectra before and after sputtering thus suggest that the carbide and the niobium oxynitride are constituents of the film interior, whereas Nb₂O₅ is confined to the surface.

b. C 1s core-level spectra The C 1s region [Figure 2(b) and (f)], in the as-received state of A_0s [Figure 2(b)], a broad peak at 284–286 eV is attributed to adventitious carbon (C–C, C–H, and C–O) that forms on all airexposed surfaces [25, 28]. A distinct peak at approximately 283 eV is assigned to niobium carbide (Nb–C) [25]. This feature persists after sputtering, indicating that it originates from the film. At the surface, the Nb–C peak of D_60s is about 1.5 times weaker than that of A_0s, whereas the peaks coincide after sputtering. The Nb–N signals of D_60s are weaker than those of A_0s by the same factor in the Nb 3d and N 1s regions Figure 2(a) and (Figure 2c). The suppression at the surface is therefore common to all core levels and is not specific to the carbide. The Nb–C peak thus points to niobium carbide in the film, a phase not resolved in the GIXRD patterns.

c. N 1s and O 1s core-level spectra The N 1s region Figure 2(c) and (Figure 2g) is dominated by a peak at approximately 397.5 eV, assigned to nitrogen in a Nb–N bonding environment [12]. In the as-received state, the Nb–N peak of D_60s is weaker than that of A_0s as part of the common surface suppression noted above. In addition, D_60s shows a feature near 400 eV corresponding to N–O bonding [26]. This indicates that oxygen partially substitutes nitrogen at the surface of D_60s. After sputtering Figure 2(g), the Nb–N peaks of both samples coincide in position, width, and intensity, and the N–O feature has vanished. This indicates the same nitrogen content within the two films.

In the as-received state Figure 2(d), the O 1s signal of D_60s is about 3 times more intense than that of A_0s, and its maximum is shifted by about 0.6 eV to higher binding energy, which correlates to Nb2O5 as identified in the Nb 3d spectra. Hydroxyl groups and adventitious C–O species adsorbed during air exposure contribute to the same envelope and are not resolved here [29]. After sputtering Figure 2(h), the two profiles overlap in terms of position and intensity. This indicates the same oxygen content within the two films. This oxygen is bound to niobium and present at low concentration, as shown by the niobium oxynitride contribution that persists in the Nb 3d spectra.

Electrical characterization

Above Tc

Sample	$T_\mathrm{c}$ (K)	$\Delta T_\mathrm{c}$ (K)	RRR	$\rho_\mathrm{opt}$ ($\mu\Omega$ cm)	$\rho_\mathrm{dc}$ ($\mu\Omega$ cm)
A_0s	12.13	0.93	0.904	213.2	537
B_20s	11.77	0.93	0.921	239.8	592
C_40s	12.19	0.98	0.918	251.9	639
D_60s	11.77	0.94	0.916	266.9	648

Table I summarizes the electrical transport parameters extracted from the $R(T)$ measurements on the 500-nm-wide nanowire structures together with the optical resistivity from spectroscopic ellipsometry [23]. The critical temperature lies within a narrow band of 11.7–12.2 K for all four samples and shows no degradation with the plasma duration. The transition width remains essentially unchanged at $\Delta T_\mathrm{c} \approx0.94$ K. All samples exhibit an increase in resistance between 300 K and $R_\mathrm{max}$. The residual resistivity ratio (RRR) is defined as $\mathrm{RRR} \equiv\rho(300\ \mathrm{K})/\rho_\mathrm{max}$, where $\rho_\mathrm{max}$ is the maximum resistivity reached just above the $T_\mathrm{c}$ onset [21, 30]. This quantity is below unity for films with negative temperature coefficient of resistivity (TCR). The measured values lie between 0.904 and 0.921 Table I. The RRR of the treated samples lies slightly closer to unity than that of the untreated film. The dc resistivity of the wires increases from 537 to 648 $\mu\Omega$ cm with the plasma exposure (20.7% increase). The optical resistivity of the unpatterned films increases from 213.2 to 266.9 $\mu\Omega$ cm (25.2%). This increase is carried by a monotonic decrease of the carrier concentration by 14.2% and of the mobility by 7.0%, consistent with the Drude relation $\rho_\mathrm{opt}=1/(Ne\mu)$ [23]. Both resistivities rise most strongly within the first 20 s of exposure. Beyond 40 s the dc resistivity saturates, whereas the optical resistivity continues to rise. The ratio of the dc to the optical resistivity remains approximately constant at $2.49 \pm0.06$ across all four samples.

Below Tc

The oxygen plasma raises the normal-state resistivity systematically but leaves the resistive transition nearly unaffected. We now examine whether this robustness extends to the current-carrying capacity of the wires. The central measured quantity is the switching current $I_\mathrm{sw}$, the bias current at which the nanowire abruptly leaves the zero-resistance state on the forward branch of the hysteretic current-voltage characteristics. It is read directly from the recorded sweeps and involves no modeling. Two consecutive sweeps were recorded at each temperature. Premature switching can only lower the measured current, so the larger of the two values was retained. Points with $I_\mathrm{sw}$ below 1 $\mu$A were excluded, since such currents are comparable to the resolution of the sweep close to $T_\mathrm{c}$. For presentation the currents are converted to current densities $J_\mathrm{sw}=I_\mathrm{sw}/(wd)$ with the lithographic width $w=500$ nm and the XRR film thicknesses. The thickness of the plasma-modified surface layer cannot be determined from our data, since XRR yields only the total film thickness, which is therefore used for all current densities. At the base temperature of 4.2 K the measured switching currents are 354, 290, 378, and 351 $\mu$A, corresponding to 6.2, 4.9, 5.9, and 5.4 MA/cm$^2$. At this temperature the current density of A_0s is the highest; C_40s lies 5%, D_60s 13%, and B_20s 21% lower, without a trend in dose. A nonsuperconducting surface layer would lower the current in proportion to its thickness.

Its effect is therefore not resolved against this scatter and is treated as a common uncertainty in the following. Figure 3(a) shows $J_{\mathrm{sw}}(T)$ for all four samples. Above approximately 7 K the three oxygen-exposed samples fall progressively below A_0s, and their supercurrent vanishes between 12.3 and 12.5 K, whereas A_0s still carries a supercurrent at 13.0 K, the upper limit of the measurement. The oxygen signature thus resides in the temperature dependence of the switching current rather than in its low-temperature magnitude.

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The zero-temperature gap is obtained from the strong-coupling relation $\Delta_0 = \beta_0 k_{\mathrm{B}}T_{\mathrm{c}}$ with $\beta_0 = 2.0$, measured by terahertz spectroscopy on films from the same deposition process [33]. Applying it to each sample’s own $T_{\mathrm{c}}$ keeps the gap per-sample and assumes that the coupling strength is unaffected by the plasma, consistent with the unchanged film interior. Comparable ratios were employed for nanowires ($\beta_0 = 2.05$) [8] and measured by tunneling spectroscopy on 4–5 nm films from the same process ($\beta_0 = 2.14$) [34]. The resistivity enters as the optical value $\rho_{\mathrm{opt}}$ of Table I, since it describes the conducting film itself, whereas $\rho_{\mathrm{dc}}$ of the wires additionally contains the grain-boundary barriers and the fabrication-related contributions discussed below. The electron diffusion coefficient, $D = 0.53\ \mathrm{cm}^{2}/\mathrm{s}$, was determined from the upper critical field of an untreated film deposited with the same process (Appendix A). The same value is used for all four samples, since the XPS spectra after sputtering show the film below the modified surface layer to be unchanged by the plasma. The coherence length is $\xi= \sqrt{\hbar D/\Delta_0} = 4.07$–$4.15$ nm, and the penetration depth is $\lambda= \sqrt{\hbar\rho_{\mathrm{opt}}/(\pi\mu_0\Delta_0)} = 412$–$468$ nm (A_0s to D_60s). The high resistivity and the small diffusion coefficient place these films in the dirty limit, in which both expressions hold.

For such superconductors the appropriate temperature dependence over the full temperature range is the dirty-limit depairing current of Kupriyanov and Lukichev (KL) [35]. We fit the measured switching currents with its closed-form approximation, Eqs. (1) and (2) [36, 37],

Here $\mathrm{KL}(t)$ approximates the exact dirty-limit solution, with $\mathrm{KL}(0) = 0.41$, and $J_{\mathrm{sw}}(0)$ is the zero-temperature amplitude of the fit. The temperature scale $T_{\mathrm{c}}^{\mathrm{fit}}$ is obtained from the data alone. For each sample a straight line is fitted to $I_{\mathrm{sw}}^{2/3}$ versus $T$ using only the near-transition points $T \ge0.9T_{\mathrm{c}}^{\mathrm{fit}}$ (4–5 points per sample), and its intercept with the temperature axis defines $T_{\mathrm{c}}^{\mathrm{fit}}$. It is held fixed in the fit, so that $J_{\mathrm{sw}}(0)$ is the only free parameter. The fits describe the measured $J_{\mathrm{sw}}(T)$ with $R^2 = 0.987$–$0.999$ [lines in Figure 3(a)] and yield the zero-temperature amplitudes listed in Table II. $J_{\mathrm{sw}}(0)$ is an extrapolated fit amplitude, not a measured value. $T_{\mathrm{c}}^{\mathrm{fit}}$ exceeds the resistive midpoint by 0.6–1.6 K. A comparable offset between the supercurrent and resistive temperature scales has been reported for disordered NbTiN wires [38].

The corresponding theoretical maximum is the depairing current. In the exact dirty limit it reads [32]

and is calculated entirely from the material parameters above. Its temperature dependence follows the same dirty-limit form, Eqs. (1) and (2), with $t = T/T_{\mathrm{c}}$. The resulting depairing currents lie between 13.6 and 17.8 MA/cm$^2$, i.e., between 875 and 1012 $\mu$A (Table II). To test the temperature dependence of the switching current without material parameters we adopt the reduced representation shown in Figure 3(b), introduced for superconductor/ferromagnet bilayers [31]. The straight line through the near-transition points that defines $T_{\mathrm{c}}^{\mathrm{fit}}$ is the near-$T_{\mathrm{c}}$ limit of Eq. (1), the Ginzburg-Landau (GL) law $I_{\mathrm{sw}}(T) = I_{\mathrm{GL}}(0)(1-t)^{3/2}$ with $I_{\mathrm{GL}}(0) = I_{\mathrm{sw}}(0)/\mathrm{KL}(0)$, to which all candidate theories reduce near $T_{\mathrm{c}}$. In the coordinates $(I_{\mathrm{sw}}/I_{\mathrm{GL}}(0))^{2/3}$ versus $t = T/T_{\mathrm{c}}^{\mathrm{fit}}$, this law is the straight line $1-t$, and the exact dirty-limit KL solution of the Usadel equations saturates at 0.53 [32, 35]. A straight line fitted over a finite near-$T_{\mathrm{c}}$ window does not yet reach the asymptotic slope. A_0s and C_40s follow the dirty-limit prediction and agree with it within 4%. B_20s lies 9% below it, and D_60s lies 5% above it. All four deviations remain within 1.2 standard deviations of the extrapolation uncertainty. A saturation above the prediction means that the near-$T_{\mathrm{c}}$ part of the curve is suppressed relative to its low-temperature part. The deviation is largest for D_60s, the sample with the largest plasma dose.

The absolute scale of the switching currents is determined by the depairing efficiency $\eta= I_{\mathrm{sw}}(0)/I_{\mathrm{dep}}(0)$, the fitted zero-temperature amplitude divided by the calculated maximum. The efficiencies lie between 0.39 and 0.46 (Table II), so the wires reach less than half of their intrinsic limit. They show no systematic dependence on the oxygen dose. The collapse test normalizes to the near-$T_{\mathrm{c}}$ extrapolation of the data and requires no material parameters, whereas $\eta$ normalizes to the calculated depairing current. The two tests are therefore complementary.

Discussion

Location of the plasma-induced oxygen

The XPS spectra before and after sputtering locate the plasma-induced oxygen at the surface. The replacement of the oxynitride-terminated surface by Nb$_2$O$_5$ [Figure 2(a) and Figure 2(d)] follows the established oxidation pathway of

Sample	$I_{\mathrm{sw}}(0)$ (µA)	$J_{\mathrm{sw}}(0)$ (MA/cm²)	$I_{\mathrm{dep}}(0)$ (µA)	$J_{\mathrm{dep}}(0)$ (MA/cm²)	$\eta$
A_0s	407.9	7.16	1012	17.8	0.40
B_20s	347.6	5.89	891	15.1	0.39
C_40s	432.6	6.76	969	15.1	0.45
D_60s	405.9	6.29	875	13.6	0.46

NbN. Nb$_2$O$_5$ forms the outermost oxide and carries the growth of thicker oxides, underlain by the dielectric niobium oxynitride Nb$_2$N$_{2-y}$O$_{3+y}$ [11]. For oxidation in air the oxynitride reaches a mean thickness of about 0.4 nm and does not grow further, whereas plasma oxidation has been reported to produce a homogeneous Nb$_2$O$_5$ layer beyond 3 nm [11]. Our spectra before and after sputtering are consistent with a plasma-thickened Nb$_2$O$_5$ layer over an oxynitride that remains in place. Its thickness under plasma exposure is not established here. Nb$_2$O$_5$ is one of the thermodynamically stable phases of the Nb–O system [39] and was not detected at the A_0s sample. This suggests that its formation requires a stronger oxidation than the exposure to air or to residual oxygen during the deposition. A comparative oxidation study of sputtered NbN films supports this. Under controlled oxidation at up to 200 °C the oxide on NbN saturates near 2 nm, air-stored films carry about 3 nm, and only plasma oxidation grows the oxide beyond 8 nm, with nitrogen leaving the oxidized layer [40]. The plasma therefore drives the surface within one minute to a state at or beyond the endpoint of natural aging. Spectroscopic ellipsometry on the same films shows an additional absorption band near 4.9 eV that appears only after the plasma treatment and has been assigned to the oxidized surface region [23].

The surface oxide leaves no trace in XRD [Fig. 1]. An x-ray amorphous surface layer does not contribute to the diffraction pattern, which explains why no additional reflections appear although the film thickness increases. An increasing oxygen content in Nb–O–N films has been reported to change the structure from a columnar crystalline microstructure toward x-ray amorphous niobium oxynitride phases [41]. The smaller crystallite size of D_60s may reflect a reduced coherent NbN thickness after the surface oxide has formed.

In granular NbN, the grain boundaries host dielectric Nb$_2$O$_5$ and niobium oxynitride [11]. With crystallites of 5.5–7 nm, our films provide a dense network of such boundaries. The niobium oxynitride found in the film is therefore a grain-boundary oxide formed during growth. Since its contribution to the sputtered Nb 3d spectra is weak [Fig. 2(e)], the oxynitride decorates the grain boundaries rather than enclosing the grains.

The two impurities (O, C) have different origins. The C 1s spectra show niobium carbide, whose carbon is supplied by the ligands of the metal-organic precursor and remains in the film when the hydrogen plasma does not remove them completely [9, 27]. Cubic NbC is isostructural with $\delta$-NbN and fully miscible with it, and the lattice parameters of the two end members are closely spaced ($a_{\mathrm{NbN}}=4.39$ Å [42], $a_{\mathrm{NbC}}=4.47$ Å [43]). The reflections of the two compounds therefore overlap, which explains why the carbide appears in XPS but not in GIXRD. The carbon most likely occupies the anion sublattice of the rock-salt lattice rather than forming a separate phase. The other impurity is oxygen. The precursor itself contains no oxygen. The oxygen seen in the O 1s spectra is therefore most likely incorporated from residual water and oxygen in the deposition chamber. For films from the same process, the Nb 3d intensity between the Nb–N and the Nb$_2$O$_5$ positions was previously assigned as a whole to a mixture of niobium oxide, oxynitride, and carboxide species [27]. The comparison before and after sputtering separates this mixture by location and is consistent with that picture. The plasma therefore modifies only the surface. It changes neither the grain boundaries nor the interior of the film.

Normal-state transport

The location of the oxygen at the surface constrains what the normal-state transport can show. Neither the NbN lattice nor the grain boundaries are affected, so the resistivity should rise while the critical temperature and the conduction mechanism remain unchanged. The measured transport follows this expectation (Table I). This robustness is consistent with the insensitivity of the critical temperature of a conventional $s$-wave superconductor to nonmagnetic impurity scattering [44]. Magnetic pair breaking is likewise not expected. The unchanged transition width indicates that the plasma introduces no macroscopic secondary phase or nonsuperconducting region, in agreement with the single-phase $\delta$-NbN observed by GIXRD. Disorder does suppress $T_{\mathrm{c}}$ in granular NbN, where a resistivity increase by nearly an order of magnitude lowers it from 11.7 to 5.4 K [21]. Extrapolating that suppression to the 20.7% increase observed here predicts a shift of about 0.06 K, well below the sample-to-sample scatter.

The negative TCR is characteristic of strongly disordered NbN. In granular films it has been attributed to transport limited by the grain boundaries, either by intergrain tunneling [45] or by a strongly reduced electron transmission across the boundaries [21]. In NbN these barriers are the grain-boundary dielectrics identified above, which cause the RRR below unity [11]. The dielectric itself carries no current. The conduction path is metallic within the NbN grains, and the boundary oxide acts as a thin barrier that the carriers must cross. The optical response probes the carriers inside the grains, whereas the dc measurement crosses the boundaries as well. The ratio $\rho_{\mathrm{dc}}/\rho_{\mathrm{opt}}$ is therefore a measure of the barrier contribution. That contribution is moderate. The resistivity rises by only 8 to 11% between 300 K and $T_{\mathrm{c}}$, and the resistive transition is a single step of 0.94 K. If a dielectric shell enclosed the grains completely, the wire would turn fully superconducting only at a lower temperature governed by the Josephson coupling between the grains [30]. The grains in our films are therefore well connected, and the boundary oxide adds a series resistance rather than isolating them.

The shift of the RRR toward unity for the treated samples is expected, since a constant added resistivity moves the ratio toward unity. The measured resistivity increase of 20.7% predicts RRR $\approx0.92$, in agreement with the observed values. The plasma treatment adds elastic scattering but does not change the transport mechanism. The optical response shows the same behavior. The disorder-related infrared absorption of the films weakens with the dose but stays at the same energy, a sign of additional scattering at the modified surface rather than of a different conduction mechanism [23].

The resistivity increase appears in the wires and in the optical response of the unpatterned films alike. The optical model treats the NbN layer as one homogeneous medium of the XRR thickness, so the Drude parameters are an average over the entire film including the oxidized surface [23]. The decrease of $N$ and $\mu$ with the plasma dose is explained there by oxygen bonded to niobium at the surface, which removes a few carriers and scatters the remaining ones [23]. The increase of both resistivities is therefore consistent with the surface modification, while the film below remains unchanged. The dc resistivity saturates together with the film thickness, consistent with the surface oxide as the source of the added scattering. The grain boundaries are not modified by the plasma, as established above. The surface oxide therefore adds scattering without altering the intergrain barriers, in contrast to granular sputtered NbN in which incorporated oxygen progressively strengthens the insulating barriers between the grains [22].

The ratio of the dc to the optical resistivity, $2.49 \pm0.06$, quantifies the contributions absent from the optical value, namely the grain-boundary barriers, fabrication-related contributions such as etch damage at the wire edges and deviations of the cross section from the lithographic layout, and the reduced dc conductivity of carriers whose spectral weight is shifted to finite frequency by disorder [23]. Since the chips were etched individually, these contributions could vary from chip to chip and mimic a dose effect. Their constancy shows that they do not change with the O$_2$ exposure. The dose effect resides in the material alone. Ellipsometry before the plasma step confirms that the four films had nearly the same optical and free-carrier response, so the differences after treatment are caused by the treatment alone [23].

Low-temperature switching currents

The normal state thus changes only by scattering added at the surface. The same surface layer could also reduce the cross section that carries the supercurrent. Neither the current densities at 4.2 K nor the efficiencies $\eta$ show a degradation with the dose [Fig. 3(a), Table II]. The larger $\eta$ of D_60s reflects its reduced ceiling. That of C_40s reflects its fitted amplitude, the largest of the series. Since the optical resistivity averages over the film including the oxidized surface, as noted above, the calculated ceilings of the treated samples are lower bounds and their efficiencies upper bounds, so the true values lie even closer to that of $\mathrm{A}_{0s}$.

The efficiencies (Table II) agree with the width dependence of bridges from the same PE-ALD process, which decreases from approximately 0.55 at 100 nm to 0.2 at 10 µm [37], or approximately 0.43 interpolated at 500 nm. Those ratios are evaluated at 4.2 K. Evaluating our wires there as well changes $\eta$ by at most 3%, so the comparison does not depend on the choice of temperature. Efficiencies of about one half are typical for NbN bridges [36], and for straight wires they point to vortex entry at the wire edges rather than localized constrictions as the switching mechanism [46]. The plasma treatment thus creates no new weak spots in the current path at low temperature.

The similarity between the four wires is confined to low temperature. Near $T_\mathrm{c}$ the treated wires fall below $\mathrm{A}_{0s}$ and their supercurrent vanishes earlier [Fig. 3(a)]. The collapse saturation of $\mathrm{D}_{60s}$ lies above that of the untreated sample [Fig. 3(b)]. Since the depairing current scales as $(1-t)^{3/2}$ near $T_\mathrm{c}$ but is governed by $\Delta_0$ at low temperature, a perturbation that lowers the temperature scale of superconductivity, rather than the zero-temperature condensate, reproduces this pattern of low-temperature convergence and near-$T_\mathrm{c}$ divergence. Geometric constrictions and current crowding are thereby excluded. They suppress the critical current predominantly at low temperature and become ineffective as $\xi(T)$ diverges toward $T_\mathrm{c}$ [36, 46], the mirror image of the observation, and they would moreover reduce $\eta$ with increasing dose, which is not observed. Homogeneous disorder enhancement is quantitatively insufficient as well. The resistivity increase of 20.7% predicts a $T_\mathrm{c}$ shift well below the sample-to-sample scatter, as shown above, whereas the suppression observed here amounts to at least 0.5 K in the supercurrent endpoint.

What remains is a surface mechanism. Both compounds of the oxidized surface identified above, $\mathrm{Nb}_2\mathrm{O}_5$ and the niobium oxynitride, are dielectric [11, 39]. The oxidized surface therefore carries no supercurrent and only reduces the cross section, which the low-temperature currents leave unresolved. The oxidation does not end at a sharp interface, however. Angle-resolved XPS suggests a gradual replacement of nitrogen by oxygen on approaching the surface [12, 47]. A partially oxidized but still metallic NbN layer with weakened superconductivity is therefore expected between the dielectric oxide and the intact film. For damaged, partially oxidized edges of NbN strips such a layer has been modeled as a normal or weakly superconducting metal with about twice the resistivity of the intact core [36]. In contrast to the dielectric oxide, this metallic layer can couple to the intact film below. A normal or weakly superconducting surface layer reduces the pair amplitude of the adjacent superconductor over the coherence length $\xi(T)$ by the proximity effect [24, 48]. At 4.2 K the order parameter of the core is fully developed and $\xi$ is small against the film thickness, so the reduction is negligible. Close to $T_\mathrm{c}$ the order parameter is weak and $\xi(T)$ spans the film, so the same layer suppresses the entire cross section. The thickness of this layer is expected to vary along the wire, since the oxygen penetration follows the local grain structure and the etched wire edges. The resistive transition percolates through the least degraded segments and keeps the midpoint of the intact film, whereas the supercurrent is limited by the weakest cross section and ends earlier. This reconciles the unchanged resistive $T_\mathrm{c}$ with the reduced supercurrent endpoint.

Conclusion

We studied the effect of a controlled $\mathrm{O}_2$ plasma treatment on PE-ALD NbN films with an as-grown thickness of 11.4 nm and 500 nm wide nanowires patterned from them. XPS before and after sputtering locates the plasma-induced oxygen in a surface layer, whereas the interior of the film is chemically indistinguishable from the untreated reference. GIXRD shows that the crystalline $\delta$-NbN below the surface remains intact. The total film thickness saturates between 40 and 60 s of exposure, indicating a self-limiting growth of the surface oxide. The normal-state resistivity rises by 21% (dc) and 25% (optical) with the dose, while the critical temperature, the transition width, and the conduction mechanism remain unchanged. The low-temperature transport is equally robust. The switching currents at 4.2 K and the depairing efficiencies $\eta=0.39$–0.46 show no systematic dependence on the oxygen dose. However, the current density is decreased with increasing oxygen dose, mainly in the vicinity of $T_\mathrm{c}$, where the supercurrent of the treated wires vanishes at least 0.5 K lower than that of the untreated wire. This temperature-selective suppression is consistent with a partially oxidized surface layer that acts on the intact film by the proximity effect. As the dose sets the oxygen therefore narrows the temperature range of the supercurrent from higher temperatures but does not systematically reduce the low-temperature current-carrying capacity. In the future, $T\mathrm{H}_z$ measurements will be performed to gain additional insights into the low-frequency electrodynamics of ALD-grown NbN thin films in dependence on the defects introduced by the oxygen plasma treatment. Also, $B_{c2}$ measurements will be performed and analyzed with respect to the effect of the oxygen plasma treatment on the diffusion coefficient of the superconducting carriers. Furthermore, the effect of the oxygen plasma treatment on the performance of SNSPDs will be investigated.

Acknowledgments

This work was supported in the innovation project “Infrared single-photon detection via superconducting nanowires tailored by disorder” by the Carl-Zeiss Stiftung as part of CZS Center QPhoton. The XRD facilities are partially supported by European Fond for Regional Development (EFRE) under the Project No. FKZ 2023 HSB 0025. The ALD equipment is supported by the Free State of Thuringia under the number 2025 VFE 0095 and co-financed by European Union funds within the framework of the European Regional Development Fund (ERDF).

Diffusion coefficient

The electron diffusion coefficient of Sec. III B 2 was measured on an untreated NbN film deposited with the same recipe, thickness, and substrate stack as sample A_0s and patterned into a Hall-bar structure with a 130-µm-long and 20-µm-wide channel. The measurements were performed in a variable-temperature cryostat equipped with a superconducting 6 T magnet (Cryo Industries of America). The resistance was recorded as a function of temperature at a bias current of 10 µA in magnetic fields of 0 to 6 T applied perpendicular to the film plane (Figure 4). With increasing field the transition shifts to lower temperatures and broadens. The critical temperature at each field was defined as the midpoint of the transition, the same criterion as in Sec. II. In zero field the midpoint lies at 11.55 K. Reversing the field at 1 T changes the midpoint by less than 5 mK, which confirms that the applied field carries no offset.

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The midpoints define the temperature dependence of the upper critical field $B_{\mathrm{c2}}$ (inset of Figure 4). It decreases linearly with temperature over the accessible field range. A linear fit over all seven fields yields $\mathrm{d}B_{\mathrm{c2}}/\mathrm{d}T = -2.07\,\mathrm{T/K}$. In the dirty limit the diffusion coefficient follows from this slope alone [36, 49],

which gives $D = 0.53\,\mathrm{cm}^{2}/\mathrm{s}$. The critical temperature itself does not enter Eq. (4). The 0.6 K difference between the Hall bar and the wire A_0s therefore does not affect the result. Reported diffusion coefficients of NbN films with different thicknesses and critical temperatures lie between 0.51 and 0.66 $\mathrm{cm}^{2}/\mathrm{s}$ [10], and a value of 0.56 $\mathrm{cm}^{2}/\mathrm{s}$ was obtained for a sputtered film with a critical temperature of 13.55 K [36]. The film-to-film variation of $D$ is thus small compared with the systematic band considered in Sec. IV. Extrapolating the fit with $B_{\mathrm{c2}}(0) = 0.69\,T_{\mathrm{c}} \lvert\mathrm{d}B_{\mathrm{c2}}/\mathrm{d}T\rvert$ [49] gives $B_{\mathrm{c2}}(0) = 16.6\,\mathrm{T}$ and a coherence length $\xi(0) = \sqrt{\Phi_{0}/(2\pi B_{\mathrm{c2}}(0))} = 4.5\,\mathrm{nm}$, close to the coherence length of Sec. III B 2.

References