Superconducting nitridized-aluminum thin films

In figure 1(a) we show the resistivity values at room temperature $\rho_{\mathrm{RT}}$ for the range of thin films produced, plotted as a function of the ratio of N₂/Ar flow in the process of sputtering deposition, and for two different fabrication runs (red and black markers). The blue triangle markers represent direct determination of $\rho_{\mathrm{RT}}$ averaged over several points randomly chosen across the 4' wafer scale, for which dispersion is found to be about or below 3%–5%. The resistivity estimations at the sample level based on the van der Pauw technique at chip level agree with the wafer-scale averaged values.

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The obtained data show that the addition of N₂ flow in the sputtering process clearly impacts the thin film resistivities for all flow values, with a significant increase with respect to the 0% reference thin film (pure Al) whose value is close or nearly comparable to bulk Al. The results for the two different fabrication runs of sputtered NitrAl thin films show significant reproducibility. $\rho_{\mathrm{RT}}$ steadily rises up to an order of magnitude with respect to pure Al in the range 2.5%–5%. Then, between 5% and 8.33% $\rho_{\mathrm{RT}}$ flattens. Beyond 10%, $\rho_{\mathrm{RT}}$ continues to rise, following a divergent dependence, finally displaying an electrically insulating characteristic at 15% N₂ flow, with $\rho_{\mathrm{RT}}\sim1.5~\Omega\,$cm, even visible in the surface color of the sample (see supplementary material E for more details).

In figure 1(b), we display the residual resistivity ratio, $RRR \equiv \rho_{\mathrm{RT}}/\rho_{\mathrm{4K}}$ with $\rho_{\mathrm{4K}}$ the resistiviy measured at 4 K, as function of N₂ flow down to 4 K. The decrease in RRR as N₂ is incorporated is a clear indicator of increased disorder and impurities in the thin film [45]. Between 2.5% up to 10%, $RRR\gtrsim1$. Above 10%, RRR tends to decrease below 1. This behavior is reminiscent of grAl devices [46], and it is in contrast with, e.g. NbN disordered films, where the conductivity of the material gradually decreases as disorder increases [47]. Exemplary IV curves for several samples at different temperatures are shown in figure 6 of the supplementary material.

An abrupt increase of resistivity at higher N₂ flows (figure 1(a)) is compatible with a Superconductor-to-Insulator Transition (SIT), either driven by localization of conduction electrons (Mott) or by disorder (Anderson) [48]. The values of $\rho_{\mathrm{RT}}$ displayed by the NitrAl samples investigated are in the same order of magnitude as grAl devices previously reporting a Mott insulator-like phase transition [38, 46], as well as disordered NbN and NbTiN thin films displaying an Anderson-like phase transition [47, 49].

Figure 2 shows the normalized sheet resistance curves $R_s/R_{RT, s}$ obtained for different NitrAl samples in the range between 19 mK and 300 K. As the N₂ flow is increased, we observe two different regimes which we classify according to the change in slope with temperature on the different curves, as follows:

• Metallic-like $(\mathrm{d} R_{\mathrm{s}} / \mathrm{d} T \gt 0)$: In this regime the resistance monotonically decreases as temperature decreases (RRR > 1). For the studied set of NitrAl films, the metallic regime comprises samples produced with N₂ flows between $0\%$ and $8.33\%$ or, equivalently, for samples with $\rho_{\mathrm{RT}}\lesssim~{76}~\mu\Omega\ \mathrm{cm}$.
• Transition point $(\mathrm{d} R_{\mathrm{s}} / \mathrm{d} T \sim 0)$: it is observed around the sample processed with 10% N₂ flow, which corresponds to $\rho_{\mathrm{RT}}\sim115$–${151}~\mu\Omega\ \mathrm{cm}(RRR\sim1)$.
• Insulator-like $(\mathrm{d} R_{\mathrm{s}} / \mathrm{d}T \lt 0)$: this regime comprises samples with increasing resistance as temperature decreases (RRR < 1). We include in this category samples produced with 11.67% and 13.3% of N₂ flow, or equivalently, with $\rho_{\mathrm{RT}}\gtrsim{396}~\mu\Omega\ \mathrm{cm}$. For this group of samples, we can also spot two distinctive features. For films produced with $11.67\%$ of N₂ fractional flow, the increase in resistance is quasi-linear for decreasing temperatures. On the other hand, the most resistive samples ($13.3\%$) show an accelerated, exponential-like increase of resistance as temperature is lowered.

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Below 4 K, all NitrAl samples in the 2.5%–13.3% N₂ flow range show a normal-to-superconducting state transition at varying $T_{\mathrm{c}}$ values. Figure 3(a) shows the suppression of resistance at the transition temperature $T_{\mathrm{c}}$ for samples with different N₂ flow fractions. We take the definition of $T_{\mathrm{c}}$ as the point where the resistance drops $50\%$ with respect to the onset point of R(T) [50]. We did not observe the superconducting transition above 19 mK for sample $13.33\%$ produced in the second run of fabrication (r2), indicating that the SIT may lie close to that process N₂ flow value.

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In several samples we have observed an increase of 20%–30% of the resistance prior to the transition to the superconducting state. Such a peak appears only for particular combination of current and voltage probes. Annex IV B 2 gives more details about this feature, which we attribute to the disordered nature of the thin films.

Figures 3(b) and (c) summarize the obtained critical temperatures as a function of N₂ flow and $\rho_{\mathrm{RT}}$, respectively. Overall, the trend of $T_{\mathrm{c}}$ values changes non-monotonically, with most samples exceeding the $T_{\mathrm{c}}$ of pure Al (dashed gray-line). The highest $T_{\mathrm{c}} = 3.38\pm{0.01}$K is observed at 5% N₂ flow [51], while the 13.33% N₂ flow sample lies below Al with $T_{\mathrm{c}} = 0.86\pm{0.02}$ K. The general shape of the $T_{\mathrm{c}}$ curve is dome-like, both in percentage and resistivity $\rho_{\mathrm{RT}}$. However, the samples with $6.67\%$ and $8.33\%$ N₂ flow do not seem to evenly follow the trend of a dome. On one hand, they display a drop in $T_{\mathrm{c}}$ in the center of the dome, and, on the other hand, their values of $\rho_{\mathrm{RT}}$ versus $T_{\mathrm{c}}$ in figure 3(c) do not follow the rest of samples. A more in-depth study of NitrAl materials at the microscopic level would be required to interpret these particular features.

We note that the dome-shape of $T_{\mathrm{c}}$ versus %N₂ in figure 3(b) roughly defines three regions: increasing $T_{\mathrm{c}}$ (0%–5%), saturation of $T_{\mathrm{c}}$ (5%–10%) and decreasing $T_{\mathrm{c}}$ (10%–13.33%), which approximately correspond with the three regimes described in figure 1(a) of $\rho_{\mathrm{RT}}$ versus %N₂/Ar. This correspondence points to a possible connection between $\rho_{\mathrm{RT}}$ and $T_{\mathrm{c}}$ driven by the same mechanism, likely the disorder and/or localization of the superconducting wave function [48]. Indeed, from the data displayed in figure 2, the insulator-like behavior begins at the 10% samples.

Three different regimes of $T_{\mathrm{c}}$ versus ρ have also been observed in other disordered superconductors such as grAl [52]. In the case of grAl it is argued that a competitive effect occurs with increasing concentration of oxygen between the phase stiffness J of the superconducting condensate, the charging energy $E_{\mathrm{C}}$ for a single electron to tunnel between aluminum grains, and the superconducting gap Δ [46]. In the metallic regime, a single wave function is formed by all electrons which is characterized by a phase stiffness J, orders of magnitude above $E_{\mathrm{C}}$ and Δ [that would correspond to $\rho_{\mathrm{RT}}$ values below $\sim{40}~\mu\Omega\ \mathrm{cm}$ for our NitrAl thin films, figure 3(c)]. At the dome maximum, the phase stiffness J falls below the Coulomb repulsion [$\rho\sim{50}~\mu\Omega\ \mathrm{cm}$ in figure 3(c)]. At this point, the transition towards an insulator begins [48]. When $J\sim\Delta$, the Coulomb repulsion localizes the wave function in the grains and the material arrives at the SIT [$\rho\gt{1000}~\mu\Omega\ \mathrm{cm}$ in figure 3(c)].

This qualitative description of grAl appears to fit well to our observations with NitrAl despite that we have no evidence of the latter having a granular structure. Yet, there exist some differences. Generally, in disordered and granular superconductors the SIT is expected for resistances close to the quantum of resistance $R_{\mathrm{Q}} = h/(2e)^2 \approx 6.4~\text{k}\Omega$. For the present study, the $R_{\mathrm{4K,s}}$ threshold value for the suppression of superconductivity is $700.8 \pm 0.9$ $\Omega / \square$, which is almost an order of magnitude smaller than $R_{\mathrm{Q}}$. We note that the observations of [46] are made on thinner films (20 nm thick), which likely enhance the effects by increasing the film resistance in the normal state. For instance, we do not have evidence of features appearing at ${\sim}1.2$ K reminiscent of pure Al for the insulating films, which might derive from the core–shell structure of grAl. The thickness-dependent effects and the microscopic material description of NitrAl will be the subject of future works, where these features will be explored explicitly in more detail.

We are in the process of building a microscopic model of NitrAl, necessary to draw quantitative conclusions from the data in figure 3 to understand the dominant energy scales in each range of $\rho_{\mathrm{RT}}$, and to determine the type of SIT.

The values of $T_{\mathrm{c}}$ and $\rho_{\mathrm{4K}}$ can be used to estimate the sheet kinetic inductance ($L_{\mathrm{k,s}}$) of the films by applying the Mattis–Bardeen formula for the complex conductivity in the local, dirty limit at low frequency $(hf\ll k_{\mathrm{B}} T)$ and in the low temperature limit $(T \ll T_{\mathrm{c}})$ [53],

$$\begin{equation} L_{\mathrm{k,s}} = 0.18 \frac{\hbar R_{\mathrm{4K,s}}}{k_B T_{\mathrm{c}}}, \end{equation} \tag{ 1 }$$

where $R_{\mathrm{4K,s}}$ is the normal state sheet resistance at 4 K, $\hbar$ is the reduced Planck constant and $k_{\mathrm{B}}$ stands for the Boltzmann constant. The values of sheet kinetic inductance obtained for the NitrAl samples range between $1.31\pm 0.01$ pH/$\square$ (0% N₂) and $422.48 \pm 8.22$ pH/$\square$ (13.3% N₂). The complete set of values for $L_{\mathrm{k,s}}$, together with $T_{\mathrm{c}}$, $\rho_{\mathrm{RT}}$ and other sample parameters, are shown in table 2. This preliminary estimation of $L_{\mathrm{k,s}}$ points towards NitrAl as a material with high$L_{\mathrm{k,s}}$, especially for the most resistive samples (11.67%–13.33% N₂ flow) that reach values close to other reported superinductive materials such as grAl [54].

Table 2. Observed parameters for the different NitrAl samples measured: sample label, N₂/Ar fractional flow (%), fabrication run number, nominal thickness t, critical temperature $T_{\mathrm{c}}$, resistivity at room temperature $\rho_{\mathrm{RT}}$, and at 4 K $\rho_{\mathrm{4K}}$, estimated sheet kinetic inductance $L_{\mathrm{k,s}}$ using equation (1).

Sample	N2/Ar (%)	Run	t (nm)	$T_{\mathrm{c}}$(K)	$\rho_{\mathrm{RT}}$ ($\mu\Omega\ \mathrm{cm}$)	$\rho_{\mathrm{4K}}$ ($\mu\Omega\ \mathrm{cm}$)	$L_{\mathrm{k,s}}$ (pH/$\square$)
A	0—Al reference	2	100.0	$1.25\pm 0.01$	$2.92 \pm 0.04$	$1.05 \pm 0.05$	$0.12 \pm 0.01$
B	2.50	2	100.0	$2.30\pm 0.01$	$25.66 \pm 0.03$	$21.82 \pm 0.03$	$1.31 \pm 0.01$
C	3.33	2	100.0	$2.57\pm 0.08$	$36.67 \pm 0.03$	$32.28 \pm 0.11$	$1.72 \pm 0.06$
D	5.00	1	100.0	$3.38\pm 0.01$	$50.01 \pm 0.03$	$46.27 \pm 0.03$	$1.88 \pm 0.01$
E	5.00	2	100.0	$3.07\pm 0.02$	$42.07 \pm 0.13$	$37.50 \pm 0.04$	$1.68 \pm 0.01$
F	6.67	2	100.0	$2.85\pm 0.04$	$29.25 \pm 0.03$	$22.17 \pm 0.03$	$1.07 \pm 0.02$
G	8.33	2	100.0	$2.43\pm 0.01$	$55.88 \pm 0.03$	$48.50 \pm 0.03$	$2.74 \pm 0.01$
H	10.0	1	83.0	$2.89\pm 0.12$	$115.97\pm 0.16$	$115.63 \pm 0.03$	$6.61 \pm 0.27$
I	10.0	2	100.0	$2.74\pm 0.01$	$150.26\pm 0.03$	$156.91 \pm 0.03$	$7.88 \pm 0.01$
J	11.67	1	97.1	$2.19\pm 0.01$	$317.52\pm 0.03$	$370.11 \pm 0.03$	$23.91 \pm 0.08$
K	11.67	2	100.0	$2.02\pm 0.01$	$444.13 \pm 0.03$	$458.59 \pm 0.03$	$35.30 \pm 0.10$
L	13.33	1	94.6	$0.91\pm 0.02$	$1312.25 \pm 0.03$	$2641.66 \pm 0.05$	$422.48 \pm 8.22$
M	13.33	2	100.0	—	$2177.01\pm 0.03$	$7008.47 \pm 0.03$	—

Additionally, the critical currents $I_{\mathrm{c}}$ have been measured at base temperature for each N₂ flow value. Since these measurements were performed on thin films with no device pattern, the results only provide a qualitative understanding of the behavior of $I_{\mathrm{c}}$ in NitrAl films. The resulting values are shown in figure 4. Note that when the samples from both fabrication runs are sorted by $\rho_{\mathrm{RT}}$ (figure 4(b)) they follow an overall consistent trend, which is in contrast to the deviations between the $I_{\mathrm{c}}$ from different fabrication runs for a given N₂ flow value (figure 4(a)). For samples in the range of 8.33%–13.33% the critical current lies below that of Al, possibly indicating that the superconducting state is weakening due to the increase in disorder/localization.

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Figure 5 shows the extracted fields at which superconductivity is destroyed $B_{\mathrm{c}}$ for perpendicular $B_{\mathrm{z,c}}$ (a) and in-plane $B_{\mathrm{x,c}}$ (b) externally applied magnetic fields as function of temperature.

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At base temperature, the Al reference ($0\%$ N₂ flow) has a critical field below 0.01 T for $B_{\mathrm{z}}$ and 0.06 T for $B_{\mathrm{x}}$, as expected for thin-film Al [55]. For the subset of NitrAl samples displayed in figure 5(a), the available range of the magnet in $B_{\mathrm{z}}$ is only capable of driving the system out of the superconducting state close to the critical temperature of the NitrAl samples. On the other hand, for $B_{\mathrm{x}}$ (figure 5(b)) the increase of resilience of NitrAl to magnetic fields with respect to the Al reference sample is high but less pronounced. We observe an increase of almost a factor 7 in the $B_{\mathrm{x, c}}$ for sample $3.3\%$. For the $10\%$ sample, the available range of the magnet in $B_{\mathrm{x}}$ is not enough to destroy the superconducting state at base temperature.

Measurements of IV-characteristics as function of the applied magnetic fields and temperature can be found in figure 12 of the supplementary Material. In particular, for the 10% sample a gradual increase of resistance is observed for the largest applied fields close to the switching current of the sample. This effect is reminiscent of type-II superconductivity where such a resistance at large applied fields close to the switching current of the sample is due to vortex flow induced by the applied current [55]. In light of this connection with type-II superconductors, the observed field at which superconductivity is destroyed may be identified as $B_{\mathrm{c}} = \mu_0H_{\mathrm{c2}}$. Additional measurements under magnetic fields are needed to study the type of superconductivity displayed by NitrAl, but those are beyond the scope of this initial work.

The results obtained for NitrAl as function of the magnetic field follow the observations in other disordered superconductors [56, 57], where an increase in resistivity and superconducting gap with respect to the pure superconductor is accompanied by an increase in critical field.

Overall, there is a clear increase in the field at which superconductivity is destroyed in both axes $B_{\mathrm{z}}, B_{\mathrm{x}}$ for increasing $\rho_{\mathrm{RT}}$ in the NitrAl samples. This magnetic field resilience makes NitrAl an interesting candidate to be used in circuits where high magnetic fields are required, such as, e.g. those manipulating electron spins [39] or hybrid superconductor-semiconductor structures [58]. The behavior of NitrAl thin films under strong magnetic fields is comparable to that displayed in general by disordered superconductors, including grAl [59], NbN [47], and NbTiN [60].