  Four-point measurements using a multi-tip scanning tunneling microscope (STM)
are carried out in order to determine surface and step conductivities on
Si(111) surfaces. In a first step, distance-dependent four-point measurements
in the linear configuration are used in combination with an analytical
three-layer model for charge transport to disentangle the 2D surface
conductivity from non-surface contributions. A termination of the Si(111)
surface with either Bi or H results in the two limiting cases of a pure 2D or
3D conductance, respectively. In order to further disentangle the surface
conductivity of the step-free surface from the contribution due to atomic
steps, a square four-probe configuration is applied as function of the rotation
angle. In total this combined approach leads to an atomic step conductivity of
$\sigma_\mathrm{step} = (29 \pm 9)$ $\mathrm{\Omega}^{-1} \mathrm{m}^{-1}$ and
to a step-free surface conductivity of $\sigma_\mathrm{surf} = (9 \pm 2) \cdot
10^{-6}\,\mathrm{\Omega}^{-1}/\square$ for the Si(111)-(7$\times$7) surface.
