Stoichiometry and thickness dependence of superconducting properties of niobium nitride thin films

The current technology used in linear particle accelerators is based on superconducting radio frequency (SRF) cavities fabricated from bulk niobium(Nb), which have smaller surface resistance and therefore dissipate less energy than traditional nonsuperconducting copper cavities. Using bulk Nb for the cavities has several advantages, which are discussed elsewhere; however, such SRF cavities have a material-dependent accelerating gradient limit. In order to overcome this fundamental limit, a multilayered coating has been proposed using layers of insulating and superconducting material applied to the interior surface of the cavity. The key to this multilayered model is to use superconducting thin films to exploit the potential field enhancement when these films are thinner than their London penetration depth. Such field enhancement has been demonstrated in MgB2thin films; here, the authors consider films of another type-II superconductor, niobium nitride (NbN). The authors present their work correlating stoichiometry and superconducting properties in NbN thin films and discuss the thickness dependence of their superconducting properties, which is important for their potential use in the proposed multilayer structure. While there are some previous studies on the relationship between stoichiometry and critical temperature TC, the authors are the first to report on the correlation between stoichiometry and the lower critical field HC1.


I. INTRODUCTION
Linear particle accelerators currently use superconducting radio frequency (SRF) cavities made from bulk niobium (Nb).These cavities have less energy dissipation than traditional copper cavities, but have a fundamental upper limit for the electric field gradient that they can sustain in an RF field; for bulk Nb, this limit is 50 MV/m, due to the lower critical field of bulk Nb, H C1 ¼ 175 Oe. 1 In order to overcome this limitation, a multilayered superconducting-insulating-superconducting (SIS) coating applied to the inner surface of the Nb cavity has been proposed by A. Gurevich. 2The proposed coating requires thin superconducting (S) layers with lower critical field (H C1 ) and critical temperature (T C ) higher than that of the bulk Nb to shield the cavity and thus prevent early magnetic field penetration, while the insulating (I) layers are needed to impede propagation of magnetic field vortices that might form and to suppress the Josephson currents between the superconducting layers.
The ultimate goal is to have the magnetic field at the Nb interface on the inner surface of the cavity smaller than the critical field of bulk Nb.It is well-known that superconducting films thinner than their London penetration depths exhibit enhanced H C1 values in the parallel field geometry compared to bulk values; this is relevant primarily because a thermodynamically stable vortex scenario with strong RF vortex dissipation exists for films thicker than the London penetration depth, which would compromise the proposed screening of the SIS coating.This H C1 enhancement is given by where u 0 is the magnetic flux quantum, d is the film thickness, and n is the coherence length of the material, and has been recently demonstrated experimentally in MgB 2 thin films. 3iobium nitride (NbN) is an ideal candidate for the SIS model; its H C1 (200 Oe) is higher and its T C (16.2 K) is nearly twice that of Nb. 1 In this paper, we consider NbN thin films, specifically films thinner than the London penetration depth of NbN, 200 nm. 1 The films were grown on insulating substrates to simulate one SI layer from the model discussed above.We discuss the relationship between film stoichiometry and superconducting properties, as well as the thickness dependence of those properties.[6][7][8]

II. FILM GROWTH AND CHARACTERIZATION
NbN films were prepared using reactive DC magnetron sputtering in a high-vacuum system with base pressures in the range of 10 À7 Torr.Deposition was carried out using a 99.95%-purity Nb target; all films were grown on commercially available MgO(100) substrates in order to emulate the a) Electronic mail: mrbeebe@email.wm.edu insulating layers of the SIS model.We note that due to the favorable lattice matching between NbN and the chosen substrate, all the films considered grew epitaxially.We also note that one sample was capped with a thin gold overlayer to observe the effect of a protected and/or smoother surface on the DC superconducting properties of the film.
After growth, the films were characterized ex situ with x-ray diffraction (XRD) and superconducting quantum interference device (SQUID) magnetometry.The Empyrean Panalytical x-ray diffractometer used gave structural information such as lattice parameter, average out-of-plane grain size, and mosaicity; the SQUID magnetometer used is a commercially available Quantum Design magnetic property measurement system and measured both the critical temperature and the DC lower critical field of the films for the field parallel to the film surface geometry.It is important to note that all critical field values reported here are necessarily underestimates of the actual value due to the geometric constraints of the DC SQUID measurement.

III. RESULTS AND CONCLUSIONS
Table I lists the lattice parameters measured for the various films as well as the corresponding lower critical field values, ordered from smallest lattice constant to largest.Highlighted rows are films that showed an enhancement in the lower critical field compared to bulk; the films highlighted in light gray have a lattice parameter between 4.38 and 4.39 A ˚, which was considered an optimal range based on the bulk NbN lattice parameter (4.395A ˚).A high-angle 2hx scan for the 80 nm film, with lattice parameter 4.388 A ˚, is shown in Fig. 1.This scan is representative of all films highlighted in light gray.
We note here that although the 378 nm film was grown to approximate bulk conditions with a thickness greater than the London penetration depth of NbN, it still showed a slight critical field enhancement from the expected bulk value, perhaps due to some underlying remnant strain.The sample highlighted in dark gray showed the best field enhancement-an increase over bulk of 1400 Oe, 450 Oe more than an uncapped sample of comparable thickness-likely due to the gold overlayer.In addition to protecting the surface from further degradation after exposure to ambient conditions, such an overlayer has been predicted to smooth out surface roughness, which would lead to improved DC superconducting performance by minimizing magnetic field pinning  sites. 9This result is encouraging, although an alternative capping layer must be considered in order to also offer SRF advantages.
We can now explore the relationship between microstructure and the superconducting properties of films with comparable lattice parameter, i.e., between 4.38 and 4.39 A ˚, and consider the lower critical field enhancement as a function of film thickness.Figure 2(a) shows the H C1 enhancement predicted by Eq. ( 1) over the range of film thicknesses given in Table I, with a coherence length of 4 nm. 1  films can exhibit strain and other microstructure defects due to lattice mismatch with the substrate and the specific growth mode followed upon the early nucleation stage.Additionally, as mentioned in Sec.II, the H C1 values measured are underestimates due to the geometric constraints of DC SQUID measurements, since perfect alignment of the film surface and the applied field is experimentally very difficult to achieve.In addition, these measurements are also very surface-sensitive; thus, the use of a capping overlayer as discussed above improves DC performance as indeed we observed.
We can also look at the critical temperature, T C , as a function of lattice parameter and film thickness.As seen in Fig. 3(a), there is a linear relationship between T C and the lattice parameter; this agrees well with the trend seen for the same range in lattice parameters as reported by Wang et al. and Wolf et al. 4,5 Figure 3(b) shows that there is no clear relationship between T C and film thickness; this is unsurprising, as T C is a "bulk property," i.e., for a given stoichiometry, T C does not depend on the thickness of the sample, as demonstrated in Bacon et al. 8 The large difference in the T C of the 378 nm sample is likely due to increased strain-related film defects that have propagated throughout the entire thickness of the film.Similar effects were again seen by Bacon et al., and this conclusion is further supported by the sample structure-although the lattice parameter in this sample is within the accepted range for this study, it is somewhat low for such a thick film, which should have achieved a lattice parameter closer to the bulk value. 8ther microstructure properties correlated to the critical field and critical temperature are the grain size, as calculated from the full-width-half-maximum (FWHM) of the NbN 2h-x XRD scans, and mosaicity, or degree of disorder, as obtained from the FWHM of the NbN XRD rocking curve.These are all plotted in Fig. 4, with bulk values again shown as solid black lines.Both H C1 and T C [Figs.4(a)  and 4(c), respectively] increase linearly with increasing grain size, which is expected due to less electron scattering from intergrain boundaries, while H C1 increases with decreasing mosaicity, also expected due to enhanced pinning sites that would lower the critical field in disordered structures [Fig.4(b)].As shown in Fig. 4(d), T C shows no trend with mosaicity, although films with m < 1 clearly performed better than films with larger degrees of disorder.As mentioned earlier with reference to Fig. 3(b), the sample with T C % 10 K is fairly thick and potentially has more structural defects; hence, its superconducting performance is decreased.
In conclusion, our results agree with previous reports indicating that good stoichiometry in general yields a linear trend between lattice parameter of NbN thin films and their T C and DC superconducting properties.When the lattice parameter is controlled, the expected enhancement of the critical field for films with thickness below the London penetration depth is also observed.This information enables the prediction of the quality of NbN thin films grown under similar conditions and the tailoring of such films for their use in the proposed SIS multilayer structures described above.

FIG. 2 .
FIG. 2. (a) Calculated predicted lower critical field (H C1 ) enhancement for NbN thin films, with a coherence length of 4 nm.(b) Actual H C1 values for the films considered here, with the theoretical curve shifted to show that the films fit the trend.The H C1 for bulk NbN, 200 Oe, is marked with a solid black line.
FIG. 3. Critical temperature, T C , as a function of (a) lattice constant and (b) thickness.The bulk value, T C ¼ 16.2 K, is shown as a solid black line.In (a), the linear trend is indicated by the dashed fit line.

TABLE I .
Lattice parameters and lower critical field values for the films studied here, as well as the corresponding bulk values.