Breakdown of Eliashberg theory for 2D superconductivity in the presence of disorder.

We have performed tunneling measurements on ultrathin homogeneous strong coupled superconducting Pb films in the regime where T sub c varies with sheet resistance. The energy gap DELTA and the strong coupling corrections to the density of states have been measured as a function of the sheet resistance R sub square. We conclude that the standard picture of enhanced Coulomb repulsion with increasing sheet resistance is too naive and, in the presence of disorder, an analysis more sophisticated than Eliashberg theory is necessary.