Optimization of the superconducting properties of NbTiN thin films by variation of the N₂ partial pressure during sputter deposition

Niobium-titanium nitride (NbTiN) is one of the robust superconducting (SC) systems among the conventional s-wave superconductors [1] for fundamental research and applied superconductor technologies. In the fundamental research, ultra-thin films of NbTiN with a thickness of the order of coherence length (ξ) and lower manifest interesting properties such as superconductor-to-insulator transition (SIT) [2], charge Berezinskii–Kosterlitz–Thouless transition [3], the SIT behavior with quantum phase slips in 1D nanowires [4], etc. On the technological side, NbTiN has a large-scale application in fields such as tunnel junction mixers [5], SC–insulating–SC junctions [6, 7], and SC hot-electron bolometers (owing to its higher energy gap) [8], among others. NbTiN is also a preferred candidate for coplanar waveguide SC resonators [9] and applications-like SC nanowire single-photon detectors (SNSPDs) [10–14]. NbTiN is a ternary alloy and is a complete homologous system wherein the ratio of Nb to Ti is flexible to any value from 0 to 1 (Nb_x Ti_{y −x} N). On the lower end of the alloy phase diagram, the end product is TiN, while at the higher end of the alloy phase diagram, NbN precipitates. The T_C of NbTiN is ∼16 K [15] and is comparable to that of NbN, and has got a relatively large penetration depth (∼260 nm) [16]. Because of its large λ values, the system is a good candidate for studies related to fluctuations of SC properties in two- and one-dimensions. Strain free NbTiN thin films can be grown over the lattice-matched substrates by reactive magnetron sputtering [17, 18]. Owing to the unprecedented interest in NbTiN for SNSPD application with very high detection efficiency and other characteristics required for single photon detection, the system has been going through intense scrutiny from the device fabrication and integration point of view with respect to quantum-enabled technologies [19].

High-quality NbTiN films can be grown by many methods such as CVD [20], MBE [21], ALD [22], reactive sputtering techniques [23], etc. In the reactive sputtering technique (which is the most common one for thin film fabrication) one can start with co-sputtering using Nb and Ti targets and converting them to Nb_x Ti_{y −x} N with a desired Nb/Ti ratio suiting different applications under optimized sputtering conditions. Reactive sputtering can also be done using a fixed Nb_x Ti_y target and optimizing the sputtering conditions to get Nb_x Ti_y N [24]. In the latter case, though the Nb/Ti ratio in the final product is almost fixed, the ratio depends on the sputtering conditions. Optimization of the sputtering conditions is required to get the best SC properties. The SC properties of NbTiN also depend on the thickness of the film [25], carrier composition [23], growth temperature [15] sputtering power [26], and the substrate material [24]. The final stoichiometry of Nb and Ti in NbTiN also plays an important role in deciding the SC properties of the system [2, 20]. The T_C of Nb_1−x Ti_x depends on the ratio of Nb/Ti, and a maximum T_C ∼17 K is reported for the Ti content of x = 0.34 [27, 28] which is close to the bulk T_C of 18 K. T_C also depends on the substrate [29] and substrate temperature used for deposition. Yu et al [15, 30] have obtained a T_C of 16.2 K for NbTiN on SiO₂, wherein the substrate was kept at 450 °C. In comparison, the room temperature (RT) deposition yielded a T_C of ∼11 K only. Similarly, deposition at 600 °C on copper cavity by Di Leo et al [31] have shown a T_C of 17 K, which is very close to the bulk T_C value, here the Ti content is 0.45 compared to the report by Yu et al. There are also reports, wherein T_C of ∼15 K has been reported for NbTiN film of thickness ∼150 nm or higher and with N₂ partial pressure in the range of ∼20% or higher [11, 24]. For SNSPD applications, devices are to be fabricated from SC films of thickness in the 2D regime, which for NbTiN films falls in the range of 10–20 nm. Moreover, NbTiN is one of the most studied systems for SNSPD applications as its performance indicators with respect to detection efficiency and jitter time are comparable or better than other systems such as MoSi, WSi, NbN etc [19, 32]. The present study is conducted to optimize the SC properties of NbTiN thin films towards the development of SNSPDs and to complement the existing literature on the deposition conditions and subsequent formation of NbTiN, specifically with respect to the role of N₂ content (nitrogen partial pressure) in the chamber to transform Nb_0.7Ti_0.3 to Nb_x Ti_y N to get the best SC properties. The depositions were performed by maintaining a substrate temperature of 600 °C during the deposition to promote epitaxial growth and crystalline nature of the films. Nevertheless, a comparison has been done with RT deposited samples for the SC and the structural properties of the thin films including the chemical content evaluation by XPS analysis. For comparison with RT deposition, we have chosen the samples towards the lower end of the N₂ partial pressure. The evaluation of the structural and SC properties was carried out by high-resolution x-ray diffraction (HRXRD) and XPS analysis and electrical transport measurements using Physical Property Measurement System (PPMS). We report a T_C as high as 15.77 K for the films deposited with an optimal N₂ partial pressure of 6.8% using MgO as the substrate. XPS analysis shows the availability of Ti ions for the RT deposited samples which hints at the incomplete reaction kinetics of conversion of NbTi to NbTiN at RT deposition. An analysis of the magneto-transport behavior with respect to thermally activated flux flow (TAFF) models from the onset of SC transition to the zero-resistance state is carried out to understand the role of magnetic field on the transition region and its suitability towards SNSPD applications.

NbTiN thin films were grown on MgO (001) single-crystal substrates by reactive DC magnetron sputtering with a base pressure of ∼2 × 10⁻⁷ mbar. The depositions were performed at a temperature of 600 °C to ensure crystallinity and phase conversion from NbTi to NbTiN. We used Nb_0.7Ti_0.3 target to grow Nb_x Ti_y N thin films. The phase conversion from Nb_0.7Ti_0.3 to Nb_x Ti_y N was aided with the help of controlled flow of nitrogen and argon into the chamber using calibrated mass flow controllers. Before deposition, substrates were annealed at ∼750 °C to get rid of contaminants. Sputtering was performed at a DC power of 80 W, for different nitrogen partial pressures such as 5.8% (S1), 6.8% (S2), 8.5% (S3), 12.5% (S4), 13.51% (S5), and 15.15% (S6) which were maintained by flowing a mixture of N₂ and Ar gas into the chamber. As there are reports on the deposition of NbTiN through DC magnetron sputtering at RT [12, 24] for our own reference and for comparative studies, we also have performed RT deposition of NbTiN films by selecting two conditions on the lower end of the N₂ concentration (i.e. for the conditions of S1 and S2). Films were grown with a thickness of 50 nm which was controlled by deposition time and rate and was further confirmed with a thickness profiler (Model—NanoMap-500LS). Structural characterization and the transport properties of the films were studied using HRXRD (X' Pert PRO PANalytical) and PPMS (Cryogenic), respectively. XPS studies were used to determine the chemical composition of the films and for the estimation of residual oxygen content due to native oxidation or that may remain due to oxidation of unreacted species remaining due to partial reaction during deposition. The SC properties of the samples were evaluated by measuring resistance as a function of temperature and magnetic field up to 5 T. RT hall measurements were performed for all the samples to estimate the carrier density, Hall coefficient, density of states, and Fermi velocity etc. A detailed description of the samples, preparation conditions, and their SC properties and physical parameters obtained from the Hall measurements are given in table 1.

Table 1. The physical parameters obtained from room temperature Hall measurements and superconducting properties of NbTiN thin films prepared with varying N₂ partial pressure during sputter deposition.

Sample	N2 partial pressure (N2/(Ar + N2)) (%)	Resistivity $\left( {{{10}^{ - 7}}\Omega \cdot {\text{m}}} \right)$	Carrier density $({10^{28}}\;{{\text{m}}^{ - 3}})$	Hall coefficient $({10^{ - 11}}{{\text{m}}^3}{{\text{C}}^{ - 1}})$	KF $({10^{10}}{{\text{m}}^{ - 1}})$	VF $\left( {{{10}^6}{{\left( {{\text{m}}\;{\text{s}}} \right)}^{ - 1}}} \right)$	$\begin{gathered} \ell \hfill \\ \left( {{{10}^{ - 9}}{\text{m}}} \right) \hfill \\ \end{gathered}$	D $\left( {{{10}^{ - 5}}\left( {{{\text{m}}^{\text{2}}}\;{{\text{s}}^{ - 1}}} \right)} \right)$ (From Hall measurements)	N (0) $\left( {{{10}^{47}}_{{\text{states}}}{{\text{m}}^{ - {\text{3}}}}\;{{\text{J}}^{ - 1}}} \right)$	TC (K)	ΔT (K)	D $\left( {{{10}^{ - 5}}{{\text{m}}^2}\;{{\text{s}}^{ - {\text{1}}}}} \right)$(from low temperature transport data)	$\xi$ (0) nm	${\Theta _D}$ (K)
S1	5.88	4.153	8.67	7.20	1.36	1.58	2.50	13.2	1.13	15.26	0.18	9.1	4.22	571.25
S2	6.67	3.379	11.62	5.36	1.51	1.75	2.53	14.8	1.25	15.77	0.14	9.0	4.12	571.03
S3	8.51	5.227	8.21	7.59	1.34	1.55	2.06	10.7	1.11	15.01	0.09	7.4	3.83	572.21
S4	12.5	7.915	6.92	9.01	1.27	1.47	1.52	7.48	1.05	14.10	0.35	6.4	3.67	572.57
S5	13.51	7.693	5.76	10.82	1.19	1.38	1.77	8.19	0.99	13.97	0.38	6.6	3.69	572.83
S6	15.15	7.848	5.52	11.31	1.17	1.36	1.79	8.14	0.97	13.95	0.32	6.1	3.61	572.84
S1 RT	5.88	14.510	7.17	8.71	1.28	1.48	0.81	4.03	1.06	10.8	0.13
S2 RT	6.67	17.642	6.83	9.13	1.26	1.46	0.69	3.37	1.04	10.5	0.18

Figure 1 shows the HRXRD pattern of all the samples (samples deposited at RT and at 600 °C along with the deposition conditions) for the 2θ range from 30° to 100°. Epitaxial growth Nb_xTi_yN is evident for the samples deposited at 600 °C, which is confirmed with the observed diffraction peaks of the oriented planes with respect to the substrate such as (200) and (400). It is also noteworthy that the respective positions of the (200) and (400) peaks shift towards lower angles except for the sample S2 (for which the peak position is shifted relatively towards the higher angles) indicating an induced strain (residual stress) with respect to the N₂ variation. In comparison, the RT deposited samples do not show any peaks of Nb_xTi_yN or any other phases such as NbN, TiN or NbTi etc. This shows that the nitridation process of NbTi to NbTiN is not effective for the RT deposited samples, the deposited film remains as mostly amorphous; wherein the diffraction peaks corresponding to the substrate only appear. The lattice constants of the samples with respect to N₂ variation were calculated assuming a cubic δ-(Nb, Ti)N (Fm3m) phase (following the JCPDS file 04-002-7196 for the NbTiN) [20] which are plotted in figure 2 along with other sample parameters such as T_C, B_C2(0), and relative intensities of the (200) and (400) peaks representative of induced texture (epitaxial growth of the sample). The variation of the lattice constant with respect to N₂ content is nonlinear. While the sample S2 shows the smallest lattice constant which is in agreement with the literature [23], as the N₂ content increases, the lattice constant also increases gradually and gets saturated towards higher N₂ content. The sample S1, which has a lesser nitrogen content also has a lattice constant higher than that of the S2. Reported studies indicate the possibility of forming hexagonal and cubic phases of NbTiN [20], depending on the deposition temperature and N₂ content. For the present study, the XRD data closely matches with the cubic phase. Further analysis such as HRTEM, in-plane XRD scans etc are required to confirm the co-existence of cubic and hexagonal phases, which is beyond the scope of the current article. Though there are several phases of NbTiN, the cubic phase with rock salt crystal structure is reported to have a higher T_C of ∼16 K [23]. The XRD intensity ratio of (200) and (400) peaks are the highest for the S2 condition and decreases as the N₂ content increases in the chamber. S1 also shows a lower intensity compared to S2. This indicates that the S2 condition is more favorable for the epitaxial growth of NbTiN phase with respect to the present deposition conditions and the target stoichiometry. As we could not observe peaks corresponding to other diffraction planes as well as for other phases, it should be concluded that the reaction kinetics of the growth of NbTiN from Nb_0.7Ti_0.3 target with respect to the present sputtering conditions and the target bias are at the optimal level. A N₂ partial pressure within the range 5.8%–8.51% is best suited for obtaining epitaxial growth of the films.

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The chemical composition and the estimation of the oxygen content on the films were done through XPS measurements with a PHI 5000 Versa Probe III XPS utilizing Al (Kα) radiation of energy = 1486 eV. The result of XPS measurements in the form of a percentage ratio of the individual ions present in the films as well as the chemical species detected through fitting process are given in table 2. The ratio of Nb:Ti for all the samples is ∼70:30 which is roughly equal to the target stoichiometry used. The fitting of the XPS peaks showed the presence of NbN, TiN, TiN_0.9, NbO, and Nb₂O₅ in all the samples, whereas as TiO₂ appears for RT deposited samples. It is well known that both Nb and Ti are prone to oxidation on exposure to ambient atmosphere. Oxide forms such as NbO, NbO_2, and Nb₂O₅ etc are the results of native oxidation of Nb films, which act as a protective layer preventing further oxidation [33–37]. XPS studies on NbTiN thin films [38] showed the presence of native oxides such as Nb₂O₅ and TiO₂ which are due to the surface oxidation of Nb and Ti respectively. In the present case, the presence of NbO and Nb₂O₅ in all the samples can be considered as the result of native oxidation process on the surface of the films, whereas the presence of TiO₂ in the RT deposited samples hints at the availability Ti ions in these samples to form TiO₂ on contact ambient conditions. From table 2, it can be understood that the O₂ content reduces with respect to the increase of N₂ partial pressure as well as for deposition at elevated temperature. The XPS spectra recorded along with the fitting and deconvolution of the spectra to identify the individual chemical species is given as figure S1 in supplementary document.

The measurements of SC transport properties of the films were carried out using PPMS down to a temperature of 2 K and with a magnetic field of upto 5 T. We have performed resistance measurements as a function of temperature for different magnetic fields [RT(B)]. Figure 3 shows the variation of resistance as a function of temperature from 20 K down to 12 K for an applied magnetic field of 0 T, wherein the SC transition of the samples is clearly registered. T_C of the thin films was defined as the temperature at which the resistance of the film drops to 50% of the value at 20 K (R_{20 K}). A T_C as high as 15.77 K has been observed for sample S2. The overall variation of T_C for the whole variation of N₂ content in the chamber is ∼11% (15.77 K for S2 and 13.95 K for S6) when the N₂ content is varied from 5.8% to 15.15%. The RT deposited samples show a much lesser T_C (11 K, for S1RT, and 10.6 K for S2RT samples), a T_C enhancement of ∼30% is visible with respect to the high temperature deposition. The observed T_C for RT deposited samples is in agreement with that reported by Jia et al [13], wherein a T_C of ∼10 K has been observed for NbTiN samples deposited on Si and SiO_x -Si substrates, but the N₂ partial pressure used by them is ∼16.66%, which is higher than what we have used in the present study. In a similar report, Yu et al [15] have found that deposition at higher temperature will enhance the T_C from about 12 K (for RT deposited samples) to ∼16 K (for samples deposited at 450 °C) compared to the samples deposited at RT. In both the above studies the N₂ partial pressure used for deposition is ∼20%, which is much higher than the range used in the present study. In a similar study, by Makise et al [24] have reported a T_C ∼ 15 K for RT deposition on substrates such as MgO, Al₂O₃ and fused quartz, wherein they have reported crystalline growth for films of thickness in the range ∼150–300 nm. Here again the N₂ partial pressure under investigation is from ∼20% and above. In contrast, [24] reports a linear dependence of lattice constant with respect to an increase in the partial pressure of N₂ with respect to all the substrates involved, whereas in the present case the optimum condition shows lower lattice constant compared to the rest of the conditions. Compared to the earlier reports on the RT depositions of NbTiN [11, 13, 24], we obtained amorphous films for deposition at RT, this presumably could be due to the lower thickness (50 nm) of the films opted for the current study. From figure 3, it can be seen that the T_C of the NbTiN thin films increases initially with respect to N₂ content upto S2, and then decreases thereafter. One can see that the variation of T_C follows the same trend as that of the variation of XRD peak intensities of the oriented planes [(200) and (400)]. ΔT_C of the samples (ΔT_C = T_C-90−T_C-10), wherein T_C-90 and T_C-10 are the temperatures at which the resistance drops to 90% and 10% of the normal state resistance (R_{20 K}) were also estimated from the R–T plots. ΔT_C is an estimation of the quality of the SC state, with lower ΔT_C associated with a better quality of superconductivity. The values of ΔT_C are given in table 1. Samples show a relatively wider transition from the sample condition of S4 onwards, as the ΔT_C values are higher, while the samples S1 to S3 show relatively lesser ΔT_C values, with S3 having the least ΔT_C. In the inset of figure 3 is shown the normal state resistivity variation of all the samples. Resistivity is lowest for the S2 condition, while the RT deposited samples show much higher resistivity values. The other physical parameters related to the samples obtained from RT Hall measurements and the results obtained from low temperature transport measurements are given in table 1. From table 1, we can see that the carrier density, diffusion coefficient, and mean free path are higher for sample S2. In corroboration with XRD analysis, this indicates that the crystallinity of this sample is better than the rest of the conditions. It is to be noted that RT diffusion coefficients obtained from the RT Hall measurements and that obtained from the SC transport measurements at low temperature are roughly agreeing to each other with slightly elevated values obtained from RT measurements.

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Figure 4 shows the resistance variation as a function of temperature for different magnetic fields [RT(B)] of the samples in the temperature range 20 K–8 K, with an applied magnetic field of upto 5 T. The RT(B) curves are shown for selected three samples viz. S1 (figure 4(a)), S2 (figure 4(b)), and S4 (figure 4(c)). As expected, as the magnetic field is increased the T_C of the samples decreases. From the RT(B) data, B_C2(T) values were determined as a function of temperature, and the results are plotted in figure 4(d). We estimated the Ginzburg–Landau coherence length [ξ(0)] for all the samples using the expression,

$$\begin{equation}\xi\!\left( 0 \right) = \sqrt {\frac{{{\Phi _0}}}{{2\Pi {T_{\text{C}}}{{\left| {\frac{{{\text{d}}{B_{{\text{C2}}}}}}{{{\text{d}}T}}} \right|}_{T = {T_{\text{C}}}}}}}} \end{equation} \tag{ 1 }$$

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where dB_C/dT is the slope of the B_C2 versus T(T = T_C) curve, Φ_° (=h/2e) is the SC flux quantum. The B_C2(0) of all the samples were estimated by extrapolating the temperature-dependent B_C2 to the zero-temperature value. Alternatively one can use the formula B_C2(0) = Φ_°/2Πξ(0)² [39]. In figure 4(d) the solid lines are linear fit related to the Ginzburg–Landau theory [40, 41] for the temperature dependence of the upper critical field of superconductors. We also have calculated the electronic diffusion coefficient using the expression

$$\begin{equation}D = \frac{{ - 4{k_{\text{B}}}}}{{\pi e\left| {\frac{{{\text{d}}B}}{{{\text{d}}{T_{\text{C}}}}}} \right|}}\end{equation} \tag{ 2 }$$

where k_B is the Boltzmann constant and e is the electronic charge [42].

The SC parameters deduced such as T_C, ΔT_C, dB/dT, B_C2(0), D, and ξ(0) for all samples are listed in table 1. It is evident from table 1 that the SC properties of the prepared films are dependent on N₂ partial pressure available in the chamber. Samples S1, S2, and S3 which are at the lower end of N₂ partial pressure show relatively higher T_C and lesser ΔT_C, which implies that this window is more favorable for obtaining better SC properties of the films. Samples S4 to S6 have relatively lesser T_C values with broad SC transitions and higher B_C2 values. This hints that these conditions are favorable for growing films for technological applications which require high magnetic fields and current densities.

We also analyzed the broadening of the SC transition between the T_C-ON and T_C-zero using the TAFF model [43]. TAFF follows the Arrhenius law,

$$\begin{equation}R\left( {T,H} \right) = {R_0}{e^{ - \left( {\frac{{{U_0}}}{{{K_{\text{B}}}T}}} \right)}}\end{equation} \tag{ 3 }$$

where U_o is the activation energy of vortices, R_o is the pre-exponential factor, and k_B is the Boltzmann constant. U_o can be extracted from the slope of ln(R) vs 1/T curves, and the values obtained as a function of applied magnetic field are shown in figure 5 for all the samples. In the inset of figure 5 is the corresponding Arrhenius plots of the sample S2 at different magnetic fields from where the activation energies have been estimated. It is to be noted that all the red lines in the inset of figure 5 merges to a common crossover point (T_cr) which is ∼15.5 K, and nearly matches with the T_C of this sample. TAFF behavior is dominated by the flow of flux vortex and is directly related to the flux pinning mechanisms available within the sample. The flux pinning mechanisms depend on many factors such as phase purity, defects including grain boundaries, and even the texturing of the samples (epitaxial growth of the film). In the present case there are no secondary phases present as is evident from the HRXRD analysis, but with respect to the N₂ content, the induced strain in the sample changes and also the texturing of the grains which can directly affect the TAFF behavior of the samples. So, as we evaluate the behavior of different samples using the TAFF, it is difficult to emphasize which of the above factors dominate for the apparent activation of flux Abrikosov vortices with respect to the magnetic field. This is evident from figure 5 that samples S2 and S6 are showing relatively higher activation energies in overall comparison to the other samples, while the activation energy of sample S5 is lower in comparison. The dependence of the activation energies of the other samples with respect to magnetic fields are more or less the same, which means, presumably the difference between these samples for the flow of flux Abrikosov vortices with an applied magnetic field is apparently nil. It should be noted that sample S2 shows the best T_C, while the T_C of S5 and S6 are almost the same, wherein the TAFF behavior of the S2 and S6 closely matches with U₀ values of the sample S6 are slightly higher compared to S2. Though TAFF behavior shows dependence on the N₂ content during deposition, a systematic study to understand its dependence on the individual parameters such as the quality of the films, texturing, defects, and other flux pinning mechanisms would be of interest for further analysis.

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Similarly, the T_C of a strong S-wave superconductor is governed by McMillan's equations [44]

$$\begin{equation}{T_{\text{C}}} = { }\frac{{{\theta _{\text{D}}}}}{{1.14}}{\text{exp}}\left( { - \frac{{1.04\left( {(1 + \lambda } \right)}}{{\lambda - {\mu ^*}\left( {1 + { }0.62\lambda } \right)}}} \right)\end{equation} \tag{ 4 }$$

where θ_D is the Debye temperature, λ is the effective electron–phonon coupling constant, and μ* is related to the Coulomb pseudo potential. The T_C analysis of our samples were done following a similar analysis done by Hazra et al [41]. The effective electron–phonon coupling constant λ is given by λ = N(0)U, where U is the attractive potential and N(0) is the density of states at the Fermi level. The Debye temperature θ_D is given by ${\theta _{D\, = \,}}\left( {h/{k_B}} \right){\left( {3{D_a}/4\pi } \right)^{1/3}}{\left( {Y/\rho } \right)^{1/2}}$, here D_a is the atomic density, Y is Young's modulus and ρ is the mass density. In the present case, the lattice constant varies with respect to the N₂ content, so θ_D also has direct dependence on the lattice constant. The calculated values of θ_D for all the samples are also shown in table 1 along with other sample specific parameters. Here we have taken the values of Young's modulus from the work of Arockiasamy et al [45] for the typical Nb/Ti ratio of Nb_0.75Ti_0.25. The variation in θ_D follows the variation of lattice constant, but the lattice constant is lowest for S2, while the T_C is highest for this sample. This indicates that other factors such as electron–phonon coupling constant and Coulomb pseudo potential are also to be taken into account for concluding the observed T_C variation. Nevertheless, in the present case, it should be noted that the extent of crystallinity/epitaxial growth is more dominant for the observed T_C variation compared to the intrinsic parameters which we described above. The phase conversion from Nb_0.7Ti_.03 to Nb_x Ti_y N is aided with the incorporation of N₂ in the sputtering chamber and a N₂ partial pressure window of 5.8%–8.5% is better with respect to the epitaxial growth and SC properties of the final product.

The optimization of the SC properties of NbTiN thin films with respect to the N₂ partial pressure during the sputter deposition of Nb_0.7Ti_0.3 has been studied. The N₂ partial pressure varied from 5.8% to 15.15% with respect to the Ar flow into the chamber. A T_C as high as 15.77 K has been observed (for a film of thickness 50 nm deposited on MgO substrate) for a N₂ partial pressure of 6.8% with respect to the Ar flow. The films show a signature of strain with respect to the N₂ content, wherein the lattice constant is minimum for the samples having 6.8% of N₂ content, while for other samples lattice constant shows an increasing trend with respect to the N₂ content. In comparison, the RT deposited samples have shown no signature of crystallinity of the phase formation of NbTiN, and the T_C measured for the RT deposited samples are much lower than that of the samples deposited at 600 °C. XPS analysis showed the presence of TiO₂ in RT deposited samples showing the availability of Ti ions hinting at the incomplete conversion of NbTi to NbTiN for RT deposition. We analyzed the variation of resistance in the presence of magnetic field using the TAFF model and calculated the activation energy by Arrhenius law. The flux flow mechanism in type-II superconductors exhibits complex behavior with respect to the different pinning mechanisms available. So, a conclusive picture of the variation of activation energy calculated from Arrhenius law is difficult to obtain. It is to be noted that with respect to current target stoichiometry, and other sputtering conditions for the reactive sputtering of NbTiN, N₂ partial pressure within the window of 5.8%–8.51% is found to be optimum with respect to the SC properties of the film. The findings of this study are very relevant for any attempts to fabricate 2D films and meander structures for single photon detection applications.

Pratiksha Pratap would like to acknowledge UGC, India for the research fellowship and AcSIR, India for PhD registration. Financial support is acknowledged from DST through the QuEST(Q-65) project and from CSIR through the FCP project. Authors acknowledge Dr Manju Singh and Dr Rajib Rakshit for initiating this work at CSIR-NPL. They thankfully acknowledge Professor Ramesh Chandra from IIT-Roorkee for providing the XPS facility.

All data that support the findings of this study are included within the article (and any supplementary files).