We calculate the critical temperature Tc and the superconducting energy
gaps Δn of a thin film superconductor system, where Δn is the
superconducting energy gap of the n-th subband. Since the quantization of
both the electron energy and phonon spectrum arises due to dimensional
confinement in one direction, the effective electron-electron interaction
mediated by the quantized confined phonons is different from that mediated by
the bulk phonon, leading to the modification of Tc in the thin film system.
We investigate the dependence of Tc and Δn on the film thickness d
with this modified interaction.Comment: 4 pages, 2 figure