  We report a quantitative low-temperature Scanning Tunneling Spectroscopy
(STS)study on the Ag(111) surface state over an unprecedented range of currents
(50 pA to 6 $\mu$A)through which we can tune the electric field in the tunnel
junction of the microscope. We show that in STS a sizeable Stark effect causes
a shift of the surface state binding energy $E_{0}$.Data taken are reproduced
by a one-dimensional potential model calculation, and are found to yield a
Stark-free energy $E_{0}$ in agreement with recent state-of-the-art
Photoemission Spectroscopy measurements.
