We calculate the effect of a static electric field on the critical
temperature of a s-wave one band superconductor in the framework of proximity
effect Eliashberg theory. In the weak electrostatic field limit the theory has
no free parameters while, in general, the only free parameter is the thickness
of the surface layer where the electric field acts. We conclude that the best
situation for increasing the critical temperature is to have a very thin film
of a superconducting material with a strong increase of electron-phonon (boson)
constant upon charging.Comment: 9 pages, 5 figure
