Single-particle electron-tunneling investigation of the phonon spectra and superconductivity of indium-tin alloys

Single-particle electron tunneling through an oxide barrier, between two metal films, Al---oxide---InₓSn_1-x, has been investigated in a study of the lattice and superconducting properties, in particular the phonon density of states, of the four distinct single-phase alloys of the In-Sn system. Measurements of the dynamic resistance of the junction, and second-harmonic response to first-harmonic stimulation across the junction, with the metal films in their superconducting state, have been analyzed using the Eliashberg gap equations and the McMillan computer program. The product function α²(ωq)F(ωq), which exhibits the structure of the density of phonon states, F(ωq), has been determined for nine intermediate In-Sn compositions. Here F(ωq) is the phonon density of states, and α²(ωq) is an electron-phonon coupling parameter which varies slowly with ωq. In the determination of the phonon spectra, the following normal-state properties of In and Sn, and their alloys have been computed: the Coulomb pseudopotential μ*; the electron-phonon interaction strength λ; and an average phonon energy 〈ωq〉. These three normal-state parameters were used to calculate the superconducting transition temperatures using the McMillan Tc equation. These calculated transition temperatures are compared with our directly measured Tc's and with previously measured values.