Ultrathin epitaxial NbN superconducting films with high upper critical field grown at low temperature

Ultrathin (5–50 nm) epitaxial superconducting niobium nitride (NbN) films were grown on AlN-buffered c-plane Al2O3 by an industrial scale physical vapor deposition technique at 400°C. Both X-ray diffraction and scanning electron microscopy analysis show high crystallinity of the (111)-oriented NbN films, with a narrow full-width-at-half-maximum of the rocking curve down to 0.030°. The lattice constant decreases with decreasing NbN layer thickness, suggesting lattice strain for films with thicknesses below 20 nm. The superconducting transition temperature, the transition width, the upper critical field, the irreversibility line, and the coherence length are closely correlated to the film thickness. GRAPHICAL ABSTRACT IMPACT STATEMENT This work realized high quality ultrathin epitaxial NbN films by an industry-scale PVD technology at low substrate temperature, which opens up new opportunities for quantum devices.


Introduction
The ability to grow niobium nitride (NbN) films by different techniques and the relatively higher superconducting transition temperature (T C ) in comparison with other transition metal based superconducting materials have made NbN one of the most widely studied superconducting materials for a range of applications. For example, NbN has emerged as a preferred material for superconducting nanowire single photon detectors (SNSPD) [1][2][3][4][5]. Epitaxial NbN films have also been investigated as the superconducting electrode for Josephson junctions in superconducting quantum interference devices, superconducting qubits, and rapid single flux quantum logic circuits [6][7][8][9][10][11].
Superconducting NbN thin films have been deposited using different methods including reactive DC/RF magnetron sputtering [12,13], pulsed laser deposition (PLD) [14,15], chemical vapor deposition (CVD) [16,17], molecular beam epitaxy [18,19], atomic layer deposition [20,21], and polymer-assisted deposition (PAD) [22]. Different materials such as MgO [5,23], SiC [24,25], Al 2 O 3 [26,27] , Si [28,29], and GaAs [3,30] have been used as the substrates for the growth of NbN films. It is known that the superconducting properties (e.g. T C ) of NbN films are sensitive not only to the deposition techniques but also to the growth conditions for a given deposition technique. The substrate materials and the film thickness also play important roles in determining superconducting properties. For instance, Hazra et al. reported a T C of around 17 K for 50 nm NbN films grown by high temperature CVD at 1300°C on sapphire and AlN [16]. Zou et al. reported the growth of 18 nm epitaxial NbN film on SrTiO 3 with a T C of 14 K by PAD [22]. Linzen et al. deposited 40 nm NbN films using a plasma-enhanced atomic layer deposition, with a T C of 13.7 K [31]. The effect of the substrate materials on superconducting properties of NbN films grown by PLD has also been reported, showing a T C of 13.1 K on MgO and 15.2 K on Al 2 O 3 substrates [32]. Furthermore, the Tc of NbN films is extremely sensitive on N concentration. As indicated by Kalal et al., both deficiency or excess of N from equiatomic NbN composition could lead to a reduction in T C when reactive magnetron sputtering of Nb target at different partial pressure of N 2 was used to grow NbN films [33].
For certain applications, epitaxial NbN film is preferred. Epitaxial NbN film with a thickness of 5 nm grown by DC magnetron sputtering on GaN-buffered sapphire showed a maximum T C of 13.2 K and an upper critical magnetic field (H c2 ) greater than 15 T at 0 K [17]. On the other hand, epitaxial NbN films deposited by sputtering on MgO (001) with a film thickness > 50 nm showed H c2 around 20 T [34]. To reduce the strain effect of substrate materials on the properties of NbN films, a buffer layer between the NbN film and the substrate has been explored. NbN films with thickness close to 5 nm deposited by magnetron sputtering on c-and M-plane sapphire substrates with eitehr a Al x Ga 1−x N (x < 20%) or an AlN buffer layers respectively showed a maximum T C of 13.3 K [17,26]. TiN buffer layer on Si has also been investigated where the T C of NbN film could be improved by about 1-3 K than that on bare Si (100) substrate [29]. A monotonic decrease in T C with decreasing NbN film thickness is commonly observed when the film thickness is less than 100 nm [13,35,36]. Therefore, it is imperative to investigate the processing-structure-property relationship of the NbN films grown by a particular deposition technique, with the purpose of optimizing their performance for specific applications.
In this work, we show that wafer scale and high crystallinity superconducting NbN thin films (5-50 nm) can be epitaxially grown on AlN buffered (20 nm) c-plane Al 2 O 3 by sputtering at a substrate temperature of 400°C. The epitaxial NbN films exhibit an in-plane strain when the film thickness is less than 20 nm. The strained ultrathin ( ∼ 5 nm) epitaxial NbN film shows an upper critical field of 36 ± 2 T and an irreversibility line of 16 ± 1 T at 4.2 K, and a coherence length of 2.542 ± 0.002 nm.

Materials and methods
The AlN and NbN layered structures were deposited on 2-inch c-plane sapphire in two separate Applied Materials' 300-mm Impulse TM physical vapor deposition (PVD) chambers. Both AlN buffer layer and NbN layers were deposited via reactive ion sputtering from Al and Nb targets respectively in Ar and N 2 ambient at a substrate temperature of 400°C. The crystal structure and microstructure of NbN films with varying thickness were analyzed by x-ray analysis and scanning TEM (STEM) using highangle annular dark-field (HAADF) detector. The details of the processing parameters to grow the films, the xray analysis, TEM characterization, and superconducting property measurement can be found from the Supplementary Information.

Results and discussion
The superconducting properties of the epitaxial NbN films depend strongly on their crystalline quality. The surface and interface also play important roles in determining the superconducting properties of ultrathin NbN films. Therefore, it is essential to fully characterize the structure of the NbN films. The film orientation with respect to the single crystal c-plane Al 2 O 3 , phase purity, crystallinity, and interface roughness were characterized by x-ray diffraction including θ -2θ scans, ω-rocking curves, φ-scans, and surface reflectivity measurements. Figure 1 shows the x-ray θ -2θ scans of the films with different film thicknesses at 2θ angle around (111) diffraction of the cubic NbN. The θ -2θ scans over a wide range of 2θ angles is shown in the Figure S1 (Supplementary Information). It is noted that the (111) diffraction peak shifts to the smaller angle with increasing the film thickness. Inset in Figure 1 shows the full-width-at-halfmaximum (FWHM) of the ω-rocking curve of the (111) diffraction and the a-axis lattice parameter of the NbN thin films with different film thicknesses, where the lattice parameter is calculated from the (002) diffraction. As can be seen from the thickness dependent lattice parameter of the NbN films shown in the inset of Figure 1, the lattice parameter of NbN remains nearly constant at 4.392 Å for films with a thickness ranging from 50 to 20 nm, and then decreases monotonically to 4.365 Å (5 nm). This suggests an a-axis lattice strain of up to 1% (considering the lattice constant of bulk NbN as 4.39 Å) for the 5 nm NbN film. This can be understood by considering that the lattice constant of Al 2 O 3 is 4.785 Å. The change of lattice parameter with film thickness is further confirmed by analyzing the selected area electron diffraction (SAED) patterns (see Figure S2 in Supplementary Information). Using Al 2 O 3 (006) plane spacing as the reference, the lattice parameter evaluated from SAED patterns is 4.370 Å and 4.390 Å for 5 and 50 nm NbN films, respectively. Both (001)-oriented AlN and (111)-oriented NbN films are compressively strained inthe-plane based on the crystal structure and the epitaxial relationship between the film and the substrate. It is noted that the 5 nm NbN film may not be in coherent strain due to the extra interface roughness resulted from the AlN buffer layer as shown in Figure 2. The FWHM of the rocking curve as shown in the inset of Figure 1, on the other hand, remains almost constant with a value around 0.030°∼ 0.033°when the NbN film thickness changes from 5 to 50 nm. Such a narrow rocking curve clearly indicates that high crystallinity (111)-oriented NbN films could be deposited by a low temperature sputtering technique.
The growth of highly crystalline epitaxial NbN films at a low substrate temperature by sputtering is further confirmed by the φ-scan of the (002) NbN film and the (116) Al 2 O 3 (see Figure S3 Figure 2c shows the respective spectrum for each component, verifying the three phases. Given the heteroepitaxial nature of the NbN films, it is important to explore the thickness dependent superconducting properties of the films. Figure 3 shows the thickness dependent T C of the NbN films, where T C is determined from the peak position of the dR/dT vs. T plot and R is the resistance of the film. As can be seen from Figure 3, the T C decreases linearly from 15.3 K (50 nm film) to 11.2 K (5 nm film) with the inverse film thickness, 1/d, where d is the film thickness. Using Simonin model [37] (d) = T C,bulk (1 − d C /d), we find that the critical thickness d C where the T C of the film disappears, is 1.38 nm. The suppression of T C with decreasing thickness can be attributed to increase in lattice disorder of the NbN film [38]. It is further noted that the films show sharp transition width ( T C ) (derived from FWHM value in dR/dT vs. T plot) from 0.4 to 0.06 K by increasing NbN thickness.
Thickness dependent T C has been widely reported for superconducting materials. In particular, lattice strain can play an important role in determining T C of very thin epitaxial superconducting films. It is widely accepted that electron-phonon coupling can be much enhanced by biaxial strain, and thus a much higher T C can be induced in the biaxial strained films. For example, it has been reported that in-plane compressive strain can enhance the T C of SrTiO 3 by up to a factor of two, resulting from the strain-induced modification of phonon modes [39]. More study further revealed that both strain and disorder could control T C [40,41]. A systematic increase of T C with epitaxial tensile strain in MgB 2 films has also been reported, resulted from the softening of the bondstretching phonon mode [42]. On the other hand, it has been reported that strain can cause significant sub-lattice distortion in the lattice structure of Nb 3 Sn, and lead to reduction of its superconducting properties, primarily due to changes in the density of states at Fermi surface with a lesser contribution due to change in the phonon spectrum [43]. For superconducting NbN, the situation can be more complex since the lattice parameter can increase continuously with an increase in N concentration due to an expansion and distortion in NbN lattice caused by the interstitial incorporation of N atoms [33]. It has been reported that the lowest Raman peak in δ-NbN due to acoustic phonons shifts to higher frequencies with increasing deviation from stoichiometry [44]. This could lead to a sharp decrease in T C . The thickness dependent T C of our ultrathin NbN films may not result from the increase in N concentration and/or deviation from the ideal stoichiometry. As shown in Figure 1, the lattice parameter decreases with decreasing film thickness. Our NbN films were deposited under the same processing conditions except for the film thickness. The high crystallinity epitaxial NbN films may suggest that the surface, the interface, and the grain size can all affect the T C . Accordingly, the grain size, calculated based on the Scherrer's equation from x-ray diffraction, was found to be around 15 and 38 nm for NbN films with thickness of 5 and 50 nm, respectively. Furthermore, it is well known that the T C of a given superconductor decreases significantly when the film thickness is comparable with the coherence length of the superconductor. Given that T C is closely related to the phonon spectrum, the electronic density of state, the electron-phonon coupling, and electron-electron interaction, more detailed study is necessary to deconvolute the fundamental mechanisms that control the T C at a film thickness comparable to the superconducting coherence length.
The superconducting transition width, T C , at different applied magnetic fields is directly related to the upper critical field (H c2 ) and irreversibility field (H irr ). Figure 4(a) shows T C as a function of external magnetic field (H) perpendicular to the film surface, where the film thickness is 5 and 50 nm, respectively. It can be seen that T C shifts to lower temperatures with increasing H, as shown in Figure 4(b), regardless of the film thickness, where the field dependent resistivity vs. temperature characteristics of the 50 nm thick film is shown in Figure S4 (Supplementary Information). Importantly, T C increases with H for both films as shown in Figure 4(a). For the thinner film (5 nm), T C rises from ∼ 1.5 to ∼ 3 K as the magnetic field increases from 0 to 7 T. On the other hand, the variation of T C is much smaller and changes from ∼ 0.15 to ∼ 0.5 K for the thicker film (50 nm) when magnetic field increases from 0 to 7 T.
Both the upper critical field H c2 (at which the superconductor becomes normal) and the irreversibility field H irr (at which the superconductor ceases to carry supercurrent) are a strong function of film thickness. The H c2 and H irr at a given temperature are defined as the fields at which the resistance of the superconducting film is 90% and 10% of the normal state resistance, respectively.  extrapolate μ 0 H c2 and μ 0 H irr at liquid helium temperature, the generalized Ginzburg-Landau (G-L) model [45] is used: The generalized G-L model can best fit our data with a = 1.0, and b = 0.82 for H c2 (T) and a = 1.8, and b = 1.18 for H irr (T). The μ 0 H c2 (4.2 K) extracted from the plots is 36 ± 2 T and 60 ± 2 T for NbN films of 5 and 50 nm, respectively, while μ 0 H irr (4.2 K) is 16 ± 1 T and 57 ± 1 T for NbN films of 5 and 50 nm, respectively. From the G-L theory, the effective coherence length at 0 K can be described by ξ(0) = φ 0 /[2πH c2 (0)], where φ 0 = 2.07 × 10 −7 Gcm 2 is the magnetic flux quantum. The coherence length of the epitaxial NbN films on AlN-buffered c-plane Al 2 O 3 is ξ(0 K) =2.542 ± 0.002 nm and 2.055 ± 0.001 nm for NbN films of 5 and 50 nm, respectively. Apparently, increasing film thickness can increase μ 0 H c2 , and thus decrease the coherence length.

Conclusion
We have grown high-quality ultrathin epitaxial superconducting NbN films on c-plane Al 2 O 3 using sputtering at a substrate temperature of 400°C, where AlN is used as a buffer layer. Both x-ray diffraction and transmission electron microscopy studies reveal that the (111)-oriented NbN films are of high crystallinity. Epitaxial NbN film with a thickness less than 20 nm is under strain. For an ultrathin NbN film (5 nm), the lattice strain is about 1%. Our experimental results also indicate that the T C of (111)-oriented epitaxial NbN films decreases with the film thickness, where the T C is suggested to disappear at a film thickness around 1.4 nm. A 5 nm NbN film exhibits a T C of 11.2 K, an upper critical field of 36 ± 2 T, an irreversibility line of 16 ± 1 T at 4.2 K, and a coherence length of 2.542 ± 0.002 nm. This demonstrates the feasibility of producing high-performance epitaxial superconducting films for quantum devices using an industry-scale PVD technology.

Acknowledgements
The work at University at Buffalo (UB) was partially supported by both the SUNY Applied Materials Research Institute, a strategic alliance between the State University of New York (SUNY) and Applied Materials, Inc. and the UB's New York State Center of Excellence in Materials Informatics through the Co-Funded Projects between UB faulty and industry collaborators. D.Z. and H.W. acknowledge the support by U.S. NSF under DMR-2016453 and DMR-1565822. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
The work at University at Buffalo (UB) was partially supported by both the SUNY Applied Materials Research