We use room temperature ion beam assisted sputtering to deposit niobium nitride thin films. Electrical and structural characterizations were performed by electric transport and magnetization measurements at variable temperatures, X-ray diffraction, and atomic force microscopy. Compared to reactive sputtering of niobium nitride, films sputtered in the presence of an ion beam show a remarkable increase in the superconducting critical temperature Tc, while exhibiting lower sensitivity to nitrogen concentration during deposition. Thickness dependence of the superconducting critical temperature is comparable to films prepared by conventional methods at high substrate temperatures and is consistent with behavior driven by quantum size effects or weak localization.

Niobium nitride (NbN) has long been a material of interest for fabrication of nano-devices in the field of quantum electronics, such as superconducting nanowire single photon detectors1 and superconducting SIS tunnel junctions,2 due to its relatively high superconducting Tc, large superconducting energy gap, and ease of fabrication. However, one of the undesired features of NbN is the presence of multiple crystal structure modifications not all of which are superconducting.3 Conventional fabrication methods, such as reactive sputtering4 or CVD and thermal diffusion,5 stabilize the growth of a desired phase of NbN by carrying out the deposition at elevated temperatures, generally more than 500 °C, which makes the process incompatible with methods like lift-off, heterostructure growth with materials sensitive to heat, or fabrication of tunnel junctions, where impurity diffusion leads to interaction at the junction interface. Recently the superconductivity at high critical temperatures in hard ϵ-NbN grown at high pressure and high temperatures was discovered.6 While there exist processes capable of achieving high-Tc NbN films deposited at room temperature, such as incorporation of methane gas with RF diode sputtering,7 they lead to films with a granular or columnar void structure, resulting in a normal state resistivity well above 104μΩ cm.2,7 Use of the substrate biasing during the deposition procedure has also been demonstrated to be a viable method of room temperature deposition, but deposited films show the presence of the lower-Tc tetragonal phase of NbN, which leads to the suppression of the overall film critical temperature.8 These growth methods require extremely precise control over relative concentrations of sputtering gasses and large sputtering powers, which leads to substrate heating.9 

Use of ion beam bombardment during the deposition process is known to have dramatic impact on the microstructure of films.10,11 It leads to densification of films and increases adhesion,12 and the additional kinetic energy supplied by the ion beam allows for increased mobility of the atomic species near the surface, reducing the presence of voids that are substituted by dislocation boundaries.13,14 Also, the increase in the momentum anisotropy leads to the development of texture with preferred orientation of film grains.15–18 In this work, we explore ion beam assisted sputtering (IBAS) that combines N2 bombardment with conventional DC magnetron sputtering. We show that IBAS can be used to produce NbN thin films with superior superconducting properties even with deposition carried out with the substrate at room temperatures. We demonstrate that use of the neutralized nitrogen ion beam during DC magnetron sputtering from a Nb target leads to NbN films at relatively high superconducting transition temperatures of up to 14.5 K and with a normal state resistivity as low as 110.62 μΩ cm, without any need for substrate heating or biasing. A direct comparison of IBAS to conventional DC reactive sputtering carried out in the same chamber shows not only an increase in superconducting critical temperature Tc of NbN films, but also a large decrease in process sensitivity to nitrogen concentration, leading to more consistent results compatible with large scale fabrication. We conduct structural and electrical characterizations of the IBAS-grown non-epitaxial thin NbN films focusing on the mechanism of the suppression of superconductivity in very thin films grown on Si wafers. We find that thin films grown by IBAS have good superconducting properties down to a critical thickness of approximately 2 nm, which is comparable to films grown by conventional methods on epitaxial substrates at high temperatures. We demonstrate that the evolution of superconducting transition temperature with film thickness Tc(d) can be explained by quantum size effects or, potentially, weak localization.

NbN films were prepared by DC magnetron sputtering in a commercial ultra-high vacuum sputtering system (Angstrom Engineering).19 After transferring the silicon wafer substrate with thermally grown silicon oxide through a load-lock, the chamber was pumped down to less than 5 × 10−8 Torr before commencing the deposition procedure. Before the actual sputtering step, the substrate’s surface was treated using a low energy argon ion beam. This is done primarily to eliminate any water or organic contamination and without loss of more than 1 nm of the substrate surface.

Sputtering was carried out at 2 m Torr with Ar2 (99.9999% purity) as sputtering gas. During reactive sputtering, N2 (99.9997% purity) gas was mixed into the sputtering gas, while in ion beam assisted sputtering, nitrogen was supplied through the ion gun only. The amount of argon and nitrogen was controlled by mass flow controllers, and monitoring of residual and sputtering gasses was done by using a quadrupole gas analyzer to ensure equivalent gas mixture in the chamber for comparison of reactive and ion beam assisted sputtering.

The 3 in. diameter sputtering target consisted of 99.9999% pure Nb, and it was located 5 in. away from the substrate at a 33° angle relative to the substrate surface normal and powered at 0.18 kW from a DC magnetron power source. Sputtering rates of approximately 1 Å/s were determined from a calibrated quartz thickness monitor and confirmed after deposition by X-ray reflectometry or by profilometer measurement on a shadowmasked twin sample. A slight difference in sputtering rates is observed when compared to reactive sputtering, which is approximately 15% lower under equivalent conditions.

The ion beam source was an end-Hall ion gun,20 in which neutralization of nitrogen ions was achieved by thermionic emission of electrons from a hollow cathode. The ion gun, positioned at azimuthal 20° relative to the sputtering gun and at an angle of 40° relative to sample surface normal, was operated in constant gas flow mode to facilitate comparison with reactive sputtering, while discharge and emission currents and voltages were kept constant during deposition. As ion bombardment at energies above 300 eV is known to cause structural damage to thin films,21 the energy of the ion beam was kept at a relatively low value of 100 eV per N2 in order to minimize these effects. This translates to an ion beam power density of approximately 70 mW/cm2. Total ion beam current under these conditions was maintained at nominal 0.5 A. The value of 100 eV per N2 was deemed optimal based on comparison with depositions carried out at 50, 200, and 300 eV, which lead to maximum Tc of 12.9, 13.6, and 13.1 K, respectively. The reduction of Tc at lower energies can be explained by a decrease in mobility of adatoms and defects due to the reduction of available kinetic energy from the incoming ions.

The films were grown on polished Si substrates with native oxide without any intentional heating during deposition. Self-heating due to sputtering did not exceed 55 °C, as determined by a calibrated thermocouple built into the substrate holder assembly.

The superconducting Tc and residual resistivity ratio were measured using the standard four-probe technique in a Quantum Design, Inc. PPMS (Physical Property Measurement System). Resistive transitions of 240 nm thick NbN films deposited on the Si substrate by IBAS can be seen in Fig. 1. To better demonstrate the dependence of superconducting Tc on the concentration of nitrogen and to facilitate comparison to reactive sputtering, the superconducting transition temperatures are explicitly plotted as a function of nitrogen concentration in Fig. 2, with the general trend of both curves that follows the results in the literature:2–4,7,9 the superconducting Tc peaks and the transition width shrinks as the NbN film approaches optimal stoichiometry. However, one can clearly see a quantitative difference when comparing the two techniques. First, there is a significant difference in the highest value of the superconducting Tc, with the IBAS samples reaching 14.5 K, close to the optimum value for bulk stoichiometric NbN. Second, there is an obvious decrease in the process sensitivity toward the concentration of nitrogen in the growth chamber: one can achieve Tc > 14 K in a range of concentrations from 13% to 22%—a dramatic improvement from reactive sputtering, in which high superconducting Tc is constrained to a window of approximately 2%.2 The room-temperature resistivity of the thin films was 110.6 ± 6.6 μΩ cm, showing no noticeable trend with a N2 concentration.

FIG. 1.

Normalized resistance as a function of temperature for 240 nm thick films grown by ion beam assisted sputtering at various N2 concentrations.

FIG. 1.

Normalized resistance as a function of temperature for 240 nm thick films grown by ion beam assisted sputtering at various N2 concentrations.

Close modal
FIG. 2.

Dependence of superconducting Tc (top) of 240 nm thick films on nitrogen concentrations. Blue points correspond to ion beam assisted sputtering (IBAS), and red points correspond to reactive sputtering. Error bars denote the 90%–10% transition width. Residual resistance ration (green, bottom) is for 240 nm IBAS films. Trend lines are polynomial fits meant as guides to the eye.

FIG. 2.

Dependence of superconducting Tc (top) of 240 nm thick films on nitrogen concentrations. Blue points correspond to ion beam assisted sputtering (IBAS), and red points correspond to reactive sputtering. Error bars denote the 90%–10% transition width. Residual resistance ration (green, bottom) is for 240 nm IBAS films. Trend lines are polynomial fits meant as guides to the eye.

Close modal

We confirmed close to optimal stoichiometry for the phase with the highest Tc using X-ray diffraction (Fig. 3). We observe prominent peaks of the cubic δ-NbN, without any presence of the non-superconducting phases, such as the common δ′-NbN phase.22 

FIG. 3.

X-ray diffraction pattern of a 500 nm NbN film deposited at optimal conditions on the Si substrate. All visible diffraction peaks correspond to cubic δ-NbN. Inset: AFM scan of the film surface. The scale bar corresponds to 400 nm.

FIG. 3.

X-ray diffraction pattern of a 500 nm NbN film deposited at optimal conditions on the Si substrate. All visible diffraction peaks correspond to cubic δ-NbN. Inset: AFM scan of the film surface. The scale bar corresponds to 400 nm.

Close modal

Despite the results indicating textured films containing predominantly cubic δ-NbN phase, the superconducting Tc of the films is lower than that of single crystal NbN. This could be explained by the effects of grain boundaries suppressing the local density of states, leading to reduced total Tc, even if the intragrain Tc would be close to maximum.23,24 This effect was observed in some of our magnetization measurements, where the superconducting transition has a long tail of more than 1 K. This is further corroborated by the residual resistivity ratios RRR = R300/R20, which are all smaller than unity, an effect attributed to grain boundary scattering of conduction electrons.23 Consistent with this description, the RRR correlates with the superconducting Tc, reaching a maximum value of approximately 0.72 (Fig. 2). By correlating this value with findings in the literature, this RRR corresponds to an average grain size of approximately 25 nm,24 in agreement with values we have determined by XRD (22 nm) and AFM (mean grain width of 25 ± 5 nm) measurements. Additionally, the limited presence of voids in films deposited by IBAS might come at the expense of increased density of dislocation defects.14 This micro-structural disorder can cause additional electron scattering, increasing the film resistance and decreasing the RRR, and also potentially lead to weak localization, as discussed below in the context of dependence of critical temperature on film thickness.

To determine the upper critical magnetic field and coherence length, we carried out magnetization measurements at various fields close to superconducting Tc, where the temperature dependent Hc2(T) was defined as a field at which the magnetization vanishes. The upper critical field Hc2(T = 0 K) was calculated by extrapolation from the Werthamer-Helfand-Hohenberg formula,25 

Hc2(0)=0.69TcdHc2(T)dTTc.
(1)

The in-plane coherence length was obtained from the Ginzburg-Landau theory, where26 

Hc2(T)=Φ02πξ2(T).
(2)

Strictly speaking, this dependence should be valid only in the critical region close to superconducting Tc, but in practice, it can be applied even deep into the superconducting state. From the upper critical fields measured for a film grown at optimal conditions (Fig. 4), the extrapolated perpendicular critical field was determined to be Hc2(0) = 319 kOe and the estimated coherence length is ξ(0) = 3.2 nm, slightly smaller than the bulk value of 5 nm reported in the literature.27,28 This reduced value of ξ(0) is the result of the renormalization of coherence length due to the short electron mean-free path in disordered sputtered films.29 

FIG. 4.

Perpendicular upper critical field Hc2 measured as a function of temperature for a 240 nm thin film deposited at optimal conditions. Inset: Normalized magnetization of the same film as a function of the applied field at temperatures close to Tc.

FIG. 4.

Perpendicular upper critical field Hc2 measured as a function of temperature for a 240 nm thin film deposited at optimal conditions. Inset: Normalized magnetization of the same film as a function of the applied field at temperatures close to Tc.

Close modal

As many applications of superconducting devices necessitate for the material to be in a form of a thin film, we also study the dependence of superconducting and electronic properties as a function of film thickness. It is well known that in NbN the superconducting state is suppressed as the film becomes thin,30–32 and it is usually explained by either weak localization,33–35 electron wave leakage,36 or surface contribution to the Ginzburg-Landau free energy of the superconductor.37 

One way to determine which model best fits our experimental data is to look at the dependence of the superconducting Tc on film thickness (Fig. 5). In the electron leakage model, the electron wave function is considered to be quantized in the direction perpendicular to the sample surface. This quantization leads to reduction in the density of states and allows for the wave function to leak outside of the superconductor. The simplified theory predicts a behavior of superconducting Tc as36,38

TcTc=expbN(0)Vd,
(3)

where Tc∞ is the critical temperature of bulk, b is the characteristic length of electron wave leakage, approximately equal to the electron Fermi wavelength, and N(0)V is the BCS coupling. If we assume N(0)V = 0.32,38 the estimated b = 1.14 Å is reasonably close to the reported values for NbN. However, considering the disordered nature of sputtered films, one might want to use a version of Eq. (3) that takes into account the presence of defects and film breakup,

TcTc=exp1N(0)Vbd+cd2,
(4)

where c is a term describing contribution of defects and is typically in the range from 0 to 20 Å2. Usage of parameters reported on previous films38 leads to quantitative behavior similar to the uncorrected theory. Removing this restriction allows for a quantitatively better fit, with estimated values b = 0.73 Å and c = 2.84 Å2. The length of b is not significantly shorter than the reported values, and c falls within the expected range, meaning that the estimate is not unphysical. The difference from the values reported by Kang et al. might be explained by the difference in the microstructure of our films, as evidenced by different sheet resistances of thin films produced by our IBAS method.

FIG. 5.

Dependence of superconducting Tc on inverse film thickness. Experimental data are plotted in blue circles, and lines show best fits of different models: The green solid line is a fit of Eq. (4), the dashed orange line corresponds to a fit of Eq. (3), and the blue dashed line is a fit to Eq. (5).

FIG. 5.

Dependence of superconducting Tc on inverse film thickness. Experimental data are plotted in blue circles, and lines show best fits of different models: The green solid line is a fit of Eq. (4), the dashed orange line corresponds to a fit of Eq. (3), and the blue dashed line is a fit to Eq. (5).

Close modal

Considering the approximately linear trend of superconducting Tc(d), a variational result from modified Ginzburg-Landau theory with an added surface term could also be applied,37 

TcTc=12aN(0)V1d,
(5)

where a is the Thomas-Fermi screening length. Using this model, we can extrapolate the limiting thickness where the superconducting state vanishes as dm = 2.7 nm, which is comparable to the coherence length ξ(0) extracted from Eq. (2) and supports the notion that ion beam assisted sputtering achieves growth without a considerable amount of non-superconducting interfacial layers, even on substrates with considerable lattice mismatch. Furthermore, we can estimate the value of screening length a ≈ 0.4 nm, in good agreement with the assumption of it being on the order of lattice spacing39,40 and much smaller than the coherence length ξ(0).

More insight into the behavior of the superconducting state in thin films can be gained from the dependence of Tc on the films’ sheet resistance Rsheet. Ivry et al. proposed a phenomenological power-law dependence of the form41 

dTc=ARsheetB,
(6)

where d is the film thickness and A and B are fitting constants. This equation can be rewritten into a form

Tc=AdexpBlnRsheet,
(7)

which can be contrasted to the result derived from BCS theory,42 

Tc=ΘD1.45exp1.04(1+λ)λμ(1+0.62λ),
(8)

where ΘD is the Debye temperature, λ is the electron-phonon coupling constant, and μ describes the Coulomb repulsive interactions. When comparing Eqs. (7) and (8), one can see that the term B is related to changes in the BCS coupling N(0)V (in weak coupling limit equal to λμ) or the interaction parameters λ and μ, which would scale as B ln(Rsheet). Fitting our experimental data to Eq. (6) yields a result B = 2, different from the average value of B ∼ 1 (although still within the range of reported values41).

A more quantitative approach to study the Coulomb interactions and localization effects can also be applied. Perturbation theory for localization in 2D superconductors, developed by Maekawa and Fukuyama, yields a result for superconducting Tc in the form43 

lnTcTc=12g1N(0)e2Rsheet2π2ћln5.5ξlTcTc213g1N(0)e2Rsheet2π2ћln5.5ξlTcTc3,
(9)

where ξ is the coherence length, l is the electronic mean free path, and g1N(0) is an effective BCS coupling constant. In the dirty limit of ξl, the first term, which is due to the reduction in the density of states, becomes negligible when compared to the second term, corresponding to a vertex correction to the electron-electron interaction. Under these assumptions, the superconducting Tc reduction should have an approximately linear dependence on the film sheet resistance. While our results do show linear behavior (as seen in Fig. 6), a fit to Eq. (9) provides the effective BCS coupling constant g1N(0) = 23.62, which is an unphysically large correction to the standard BCS value of 0.32. Also, a superconductor to insulator transition can typically be driven by weak localization when the sheet resistances Rsheet are around the quantum value h4e2 6.4 kΩ,44 as can also be seen when extending our fit. Extrapolating the dependence of Rsheet vs film thickness, the critical thickness for this transition is approximately 2 nm, which is close to the estimate from Eq. (5). Alternatively, one can employ Finkel’stein results using renormalization group methods,45 

TcTc=exp1γ×1+r/2γr/41r/2γr/41/2d,
(10)

where γ=1log(kBTcτ/ћ), r=Rsheet(2π2ћ/e2), kB is the Boltzmann constant, e is the elementary charge, and τ is the electron elastic scattering time. Fitting our data to this equation yields τ = 2.43 × 10−15 s, four times smaller than the value reported in the literature.46 This difference is not surprising when one considers higher resistance of our thin films and its relation to the electronic mean-free path, which is proportional to τ.

FIG. 6.

Dependence of superconducting Tc on sheet resistance. The blue curve is a fit of the experimental data to Eq. (9), and the orange curve corresponds to a fit to Eq. (10).

FIG. 6.

Dependence of superconducting Tc on sheet resistance. The blue curve is a fit of the experimental data to Eq. (9), and the orange curve corresponds to a fit to Eq. (10).

Close modal

Both Eqs. (9) and (10) predict vanishing superconductivity at values of Rsheet that coincide with critical thicknesses extrapolated from models related to dimensionality effects [Eqs. (3), (4), and (5)], which complicates determination of the suppression mechanism. Multiple results in the literature observe the critical thickness for NbN close to 2 nm in films prepared using different growth conditions and therefore having different electronic properties,32,38,41,46–48 which might be an indication that the reduction of superconducting Tc is driven by effects related to dimensionality. However, there has been no observation of higher order effects, such as Tc oscillation with the thickness predicted by the electron leakage model, in this work or others. As Eq.(10) yields a good quantitative fit with physically reasonable values, further study is required to rule out localization effects as a mechanism for suppression of Tc, even more so, when one considers the disordered nature of sputtered films.

We have shown that NbN thin film growth using low energy bombardment with N2 during sputtering of Nb has beneficial effects on superconducting and electronic properties of the resulting NbN films. This room temperature process results in films having a resistivity as low as 110 μΩ cm, a relatively high Tc of 14.5 K, and a critical magnetic field Hc2(0) of nearly 32 T. The stoichiometric growth can be achieved in a broad range of nitrogen concentrations and does not require epitaxial growth conditions, which opens opportunities for broader application of NbN in quantum electronic devices.

Our data on ultrathin NbN films support the predictions of models of electron wave leakage (quantum size effect) or weak localization. Even on non-epitaxial substrates, superconductivity persists down to the thickness of approximately 2 nm, which also coincides with sheet resistances equal to resistance quantum, where one can potentially expect superconductor-insulator transition driven by weak localization.

The authors would like to thank Aaron Miller from Quantum Opus, LLC in Novi, MI, USA, and André Anders from Leibniz Institute of Surface Engineering in Leipzig, Germany, for stimulating discussions.

This work was supported by the U. S. Department of Energy (DOE), Office of Science, Offices of Nuclear Physics, Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-06CH11357. G.K. was supported by the Center for the Computational Design of Functional Layered Materials (CCDM), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0012575.

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