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Developing a Chemical and Structural Understanding of the Surface Oxide in a Niobium Superconducting Qubit

We report superconducting thin films of niobium have been extensively employed in transmon qubit architectures. Although these architectures have demonstrated remarkable improvements in recent years, further improvements in performance through materials engineering will aid in large-scale deployment. Here, we use information retrieved from secondary ion mass spectrometry and electron microscopy to conduct a detailed assessment of the surface oxide that forms in ambient conditions for transmon test qubit devices patterned from a niobium film. We observe that this oxide exhibits a varying stoichiometry with NbO and NbO 2 found closer to the niobium film and Nb 2 O 5 found closer to the surface. In terms of structural analysis, we find that the Nb 2 O 5 region is semicrystalline in nature and exhibits randomly oriented grains on the order of 1-2 nm corresponding to monoclinic N-Nb 2 O 5 that are dispersed throughout an amorphous matrix. Using fluctuation electron microscopy, we are able to map the relative crystallinity in the Nb 2 O 5 region with nanometer spatial resolution. Through this correlative method, we observe that amorphous regions are more likely to contain oxygen vacancies and exhibit weaker bonds between the niobium and oxygen atoms. Based on these findings, we expect that oxygen vacancies likely serve as a decoherence mechanism in quantum systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Materials Data on NbN by Materials Project

NbN is Molybdenum Carbide MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Nb3+ is bonded to six N3- atoms to form a mixture of face, edge, and corner-sharing NbN6 octahedra. The corner-sharing octahedra tilt angles range from 0–45°. There are three shorter (2.23 Å) and three longer (2.26 Å) Nb–N bond lengths. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded to six equivalent Nb3+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. In the second N3- site, N3- is bonded to six equivalent Nb3+ atoms to form a mixture of distorted edge and corner-sharing NNb6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 1°.

36 MATERIALS SCIENCE↗

Materials Data on NbN by Materials Project

NbN is Halite, Rock Salt structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Nb3+ is bonded to six equivalent N3- atoms to form a mixture of corner and edge-sharing NbN6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Nb–N bond lengths are 2.23 Å. N3- is bonded to six equivalent Nb3+ atoms to form a mixture of corner and edge-sharing NNb6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗

Materials Data on NbN by Materials Project

NbN is Tungsten Carbide structured and crystallizes in the hexagonal P-6m2 space group. The structure is three-dimensional. Nb3+ is bonded to six equivalent N3- atoms to form a mixture of distorted edge, face, and corner-sharing NbN6 pentagonal pyramids. All Nb–N bond lengths are 2.25 Å. N3- is bonded to six equivalent Nb3+ atoms to form a mixture of distorted edge, face, and corner-sharing NNb6 pentagonal pyramids.

36 MATERIALS SCIENCE↗

Materials Data on NbN by Materials Project

NbN is Molybdenum Carbide MAX Phase-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Nb3+ is bonded to six equivalent N3- atoms to form a mixture of distorted corner and edge-sharing NbN6 pentagonal pyramids. All Nb–N bond lengths are 2.23 Å. N3- is bonded to six equivalent Nb3+ atoms to form a mixture of corner, edge, and face-sharing NNb6 octahedra. The corner-sharing octahedral tilt angles are 46°.

36 MATERIALS SCIENCE↗

Materials Data on Nb4N3 by Materials Project

Nb4N3 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. there are two inequivalent Nb+2.25+ sites. In the first Nb+2.25+ site, Nb+2.25+ is bonded in a square co-planar geometry to four N3- atoms. There are two shorter (2.18 Å) and two longer (2.21 Å) Nb–N bond lengths. In the second Nb+2.25+ site, Nb+2.25+ is bonded to five N3- atoms to form a mixture of edge and corner-sharing NbN5 square pyramids. All Nb–N bond lengths are 2.21 Å. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded to six Nb+2.25+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the second N3- site, N3- is bonded to six Nb+2.25+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedra tilt angles range from 0–2°.

36 MATERIALS SCIENCE↗

Materials Data on Nb5N6 by Materials Project

Nb5N6 crystallizes in the hexagonal P6_3/mcm space group. The structure is three-dimensional. there are two inequivalent Nb+3.60+ sites. In the first Nb+3.60+ site, Nb+3.60+ is bonded to six equivalent N3- atoms to form a mixture of corner and edge-sharing NbN6 octahedra. All Nb–N bond lengths are 2.16 Å. In the second Nb+3.60+ site, Nb+3.60+ is bonded to six equivalent N3- atoms to form a mixture of distorted corner and edge-sharing NbN6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 3°. There are four shorter (2.20 Å) and two longer (2.21 Å) Nb–N bond lengths. N3- is bonded to five Nb+3.60+ atoms to form a mixture of corner, edge, and face-sharing NNb5 square pyramids.

36 MATERIALS SCIENCE↗

Materials Data on Nb3N5 by Materials Project

Nb3N5 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. there are two inequivalent Nb5+ sites. In the first Nb5+ site, Nb5+ is bonded to six N3- atoms to form a mixture of distorted edge and corner-sharing NbN6 octahedra. The corner-sharing octahedra tilt angles range from 36–57°. There are a spread of Nb–N bond distances ranging from 1.96–2.33 Å. In the second Nb5+ site, Nb5+ is bonded to six N3- atoms to form a mixture of distorted edge and corner-sharing NbN6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 20°. There are a spread of Nb–N bond distances ranging from 2.06–2.13 Å. There are three inequivalent N3- sites. In the first N3- site, N3- is bonded to four Nb5+ atoms to form a mixture of distorted edge and corner-sharing NNb4 trigonal pyramids. In the second N3- site, N3- is bonded in a distorted T-shaped geometry to three Nb5+ atoms. In the third N3- site, N3- is bonded in a distorted see-saw-like geometry to four Nb5+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on NbN by Materials Project

NbN is Wurtzite structured and crystallizes in the hexagonal P6_3mc space group. The structure is three-dimensional. Nb3+ is bonded to four equivalent N3- atoms to form distorted corner-sharing NbN4 tetrahedra. There are one shorter (1.99 Å) and three longer (2.12 Å) Nb–N bond lengths. N3- is bonded to four equivalent Nb3+ atoms to form distorted corner-sharing NNb4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on NbN by Materials Project

NbN is Tungsten Carbide-like structured and crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Nb3+ is bonded to six equivalent N3- atoms to form a mixture of edge, corner, and face-sharing NbN6 octahedra. The corner-sharing octahedral tilt angles are 44°. All Nb–N bond lengths are 2.25 Å. N3- is bonded to six equivalent Nb3+ atoms to form a mixture of distorted edge and corner-sharing NNb6 pentagonal pyramids.

36 MATERIALS SCIENCE↗

Materials Data on NbN by Materials Project

NbN is Zincblende, Sphalerite structured and crystallizes in the cubic F-43m space group. The structure is three-dimensional. Nb3+ is bonded to four equivalent N3- atoms to form corner-sharing NbN4 tetrahedra. All Nb–N bond lengths are 2.08 Å. N3- is bonded to four equivalent Nb3+ atoms to form corner-sharing NNb4 tetrahedra.

36 MATERIALS SCIENCE↗

Materials Data on Nb20N17 by Materials Project

Nb20N17 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are eight inequivalent Nb+2.55+ sites. In the first Nb+2.55+ site, Nb+2.55+ is bonded in a square co-planar geometry to four N3- atoms. There are two shorter (2.20 Å) and two longer (2.21 Å) Nb–N bond lengths. In the second Nb+2.55+ site, Nb+2.55+ is bonded to five N3- atoms to form NbN5 square pyramids that share corners with seven NbN5 square pyramids, edges with four NbN6 octahedra, and edges with four NbN5 square pyramids. There are a spread of Nb–N bond distances ranging from 2.20–2.30 Å. In the third Nb+2.55+ site, Nb+2.55+ is bonded to five N3- atoms to form NbN5 square pyramids that share corners with eight NbN5 square pyramids, edges with three NbN6 octahedra, and edges with five NbN5 square pyramids. There are a spread of Nb–N bond distances ranging from 2.21–2.31 Å. In the fourth Nb+2.55+ site, Nb+2.55+ is bonded to five N3- atoms to form NbN5 square pyramids that share corners with five NbN6 octahedra, corners with four equivalent NbN5 square pyramids, an edgeedge with one NbN6 octahedra, and edges with five NbN5 square pyramids. The corner-sharing octahedra tilt angles range from 0–4°. There are a spread of Nb–N bond distances ranging from 2.21–2.28 Å. In the fifth Nb+2.55+ site, Nb+2.55+ is bonded to six N3- atoms to form NbN6 octahedra that share a cornercorner with one NbN6 octahedra, corners with five NbN5 square pyramids, an edgeedge with one NbN6 octahedra, and edges with nine NbN5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are five shorter (2.22 Å) and one longer (2.27 Å) Nb–N bond lengths. In the sixth Nb+2.55+ site, Nb+2.55+ is bonded to five N3- atoms to form NbN5 square pyramids that share corners with three NbN6 octahedra, corners with four NbN5 square pyramids, edges with two equivalent NbN6 octahedra, and edges with six NbN5 square pyramids. The corner-sharing octahedra tilt angles range from 0–3°. There are four shorter (2.22 Å) and one longer (2.24 Å) Nb–N bond lengths. In the seventh Nb+2.55+ site, Nb+2.55+ is bonded to five N3- atoms to form NbN5 square pyramids that share corners with two equivalent NbN6 octahedra, corners with five NbN5 square pyramids, edges with two NbN6 octahedra, and edges with six NbN5 square pyramids. The corner-sharing octahedral tilt angles are 2°. There are a spread of Nb–N bond distances ranging from 2.20–2.30 Å. In the eighth Nb+2.55+ site, Nb+2.55+ is bonded to six N3- atoms to form NbN6 octahedra that share a cornercorner with one NbN6 octahedra, corners with five NbN5 square pyramids, edges with two equivalent NbN6 octahedra, and edges with ten NbN5 square pyramids. The corner-sharing octahedral tilt angles are 0°. There are a spread of Nb–N bond distances ranging from 2.21–2.26 Å. There are seven inequivalent N3- sites. In the first N3- site, N3- is bonded to six Nb+2.55+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedral tilt angles are 0°. In the second N3- site, N3- is bonded to six Nb+2.55+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the third N3- site, N3- is bonded to six Nb+2.55+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the fourth N3- site, N3- is bonded to six Nb+2.55+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedra tilt angles range from 0–8°. In the fifth N3- site, N3- is bonded to six Nb+2.55+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedra tilt angles range from 0–4°. In the sixth N3- site, N3- is bonded to six Nb+2.55+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedra tilt angles range from 0–5°. In the seventh N3- site, N3- is bonded to six Nb+2.55+ atoms to form a mixture of edge and corner-sharing NNb6 octahedra. The corner-sharing octahedra tilt angles range from 1–8°.

36 MATERIALS SCIENCE↗