  We consider effects of an externally applied electrostatic field on
superconductivity, self-consistently within a BCS mean field model, for a clean
3D metal thin film. The electrostatic change in superconducting condensation
energy scales as $\mu^{-1}$ close to subband edges as a function of the Fermi
energy $\mu$, and follows 3D scaling $\mu^{-2}$ away from them. We discuss
nonlinearities beyond gate effect, and contrast results to recent experiments.
