  The investigation of the electronic properties of semiconductor surfaces
using scanning tunnelling spectroscopy (STS) is often hindered by
non-equilibrium transport of the injected charge carriers. We propose a
correction method for the resulting systematic errors in STS data, which is
demonstrated for the well known Si(111)-(7x7) surface. The surface has an odd
number of electrons per surface unit cell and is metallic above 20 K. We
observe an energy gap in the ground state of this surface by STS at 0.3 K.
After correction, the measured width of the gap is (70 +- 15) meV which is
compatible with previous less precise estimates. No sharp peak of the density
of states at the Fermi level is observed, in contrast to proposed models for
the Si(111)-(7x7) surface.
