Stress-induced structural changes in superconducting Nb thin films

We report on the analysis of stress-induced structural changes and the formation of an omega $\left(\omega \right)$ phase in polycrystalline Nb thin films deposited on Si by high-power impulse magnetron sputtering (HiPIMS) for superconducting qubits using x-ray diffraction (XRD), transmission electron microscopy (TEM), and density-functional theory (DFT). XRD analysis indicates that internal stresses in the Nb thin films lead to the formation of $\left\{112\right\}\langle 111\rangle$ deformation twins and TEM analysis shows that $\omega$ phases nucleate at some of the twin boundaries in the Nb thin films. The size of $\omega$ phases ranges from 10 to 100 nm, which is comparable to the coherence length of Nb $(\approx 40 \mathrm{nm})$, and $\approx 1\%$ volume fraction of Nb grains exhibit this $\omega$ phase. The details of the formation mechanism and superconducting properties of the $\omega$ phases are investigated by DFT and potential roles of the $\omega$ phase in Nb as a source of decoherence in superconducting qubits are also discussed.

Figure 1

(a) ADF-STEM image of 170 nm thick Nb thin film on Si (100) substrate deposited by HiPIMS. It shows typical columnar grain structures of Nb thin films on Si substrates for films deposited with this method. (b) X-ray diffraction spectra of the Nb thin film on Si (100) and bulk Nb are displayed. It shows that Nb peaks are shifted toward lower angles from fully relaxed bulk Nb, indicating that Nb thin films are under internal stress. (c) A closer look at the Nb (110) peak shows that Nb (110) peak is shifted to lower angle by $0.5^{\text{o}}$ from relaxed bulk Nb, which corresponds to 1.1% increase of the planar distance of (110) surface normal plane of the Nb thin film on Si (100). (d) Pole figure plot of Nb $\left\{110\right\}$ taken from Nb thin film on Si (100) for a range of $\psi$ values from 0 to ${75}^{\text{o}}$ displays a Nb $\left\{110\right\}$ peak at $\psi =0$ and ${60}^{\text{o}}$. At $\psi =33.6^{\text{o}}$, we observe an additional peak that arises from twinned $\left\{110\right\}$ parallel to the surface.

Figure 2

(a) HR-TEM image of Nb grain on bcc Nb $\left[1\overline{1}0\right]$ zone axis with fully transformed $\omega$-Nb phase at $\left\{112\right\}\langle 111\rangle$ twin boundary and (b) the details of the twin boundary denoted by the square in Fig. 2 are shown. (c) FFT of the HR-TEM image of $\omega$-Nb phase in Nb demonstrates the appearance of reflection from the $\omega$-Nb phase. Three-dimensional orientation relationships (ORs) of $\omega$-Nb phase in Nb are observed, $[1\overline{1}{0]}_{\mathrm{bcc}}//\left[1\overline{2}10\right]{}_{\omega }$ and ${\left(112\right)}_{\mathrm{bcc}}//\left(\overline{1}010\right){}_{\omega }$, which is the typical orientation relationships for $\omega$ phases in bcc metals. (d) A schematic of atomic structures of the bcc/$\omega$-Nb interface in Fig. 2 is provided. We note that (0001)${}_{\omega }$ plane B of $\omega$ phase has twice the atomic number density compared to (0001)${}_{\omega }$ plane A due to the collapse of two adjacent $\left(11\overline{1}\right)$ planes from bcc Nb.

Figure 3

(a) A low magnification overview of the omega ($\omega$) phase in Nb thin film. (b) A high magnification HR-TEM image of a selected area from the surface to substrate direction in Fig. 3. An associated FFT pattern taken from the omega phase is provided as an inset and reflections from bcc Nb [113] zone axis are denoted by yellow dotted circles. Additional reflections from ($\overline{1}010$) $\omega$-Nb are seen inside the reflections from the bcc Nb on [113] zone axis. (c) Inverse FFT image is taken from the $\omega$-Nb reflections in the FFT of Fig. 3 and the morphology of the $\omega$-Nb is displayed.

Figure 4

Calculated effect of the bcc-to-$\omega$ phase transition on $T_c$. Inset figures illustrate the changing crystal structures as well as real space Fermi-level density of states contours in yellow.