We investigate the link between superconductivity and atomic vibrations in Nb${}_3$Sn films with a thickness ranging from 10 to 50 nm. The challenge of measuring the phonon density of states (PDOS) of these films has been tackled by employing the technique of nuclear inelastic scattering by ${}^{119}$Sn isotopes to reveal the Sn-partial phonon density of states. With the support of ab initio calculations, we evaluate the effect of reduced film thickness on the PDOS. This approach allows us to estimate the changes in superconducting critical temperature $T_c$ induced by phonon confinement, which turned out to be limited to a few tenths of K. The presented method is successful for the Nb${}_3$Sn system and paves the way for more systematic studies of the role of phonon confinement in Sn-containing superconductors.

• Received 6 May 2013
• Corrected 4 October 2013

DOI:https://doi.org/10.1103/PhysRevB.88.045437