  Inelastic tunneling spectroscopy of Pb islands on Cu(111) obtained by
scanning tunneling microscopy below 1K provides a direct access to the local
Eliashberg function of the islands with high energy resolution. The Eliashberg
function describes the electron-phonon interaction causing conventional
superconductivity. The measured Eliashberg function strongly depends on the
local thickness of the Pb nanostructures and shows a sharp maximum when quantum
well states of the Pb islands come close to the Fermi energy. Ab initio
calculations reveal that this is related to enhanced electron-phonon coupling
at these thicknesses.
