  An analytical N-layer model for charge transport close to a surface is
derived from the solution of Poisson's equation and used to describe
distance-dependent electrical four-point measurements on the microscale. As the
N-layer model comprises a surface channel, multiple intermediate layers and a
semi-infinite bulk, it can be applied to semiconductors in combination with a
calculation of the near-surface band-bending to model very precisely the
measured four-point resistance on the surface of a specific sample and to
extract a value for the surface conductivity. For describing four-point
measurements on sample geometries with mixed 2D-3D conduction channels often a
very simple parallel-circuit model has so far been used in the literature, but
the application of this model is limited, as there are already significant
deviations, when it is compared to the lowest possible case of the N-layer
model, i.e. the 3-layer model. Furthermore, the N-layer model is applied to
published distance-dependent four-point resistance measurements obtained with a
multi-tip scanning tunneling microscope (STM) on Germanium(100) and
Silicon(100) with different bulk doping concentrations resulting in the
determination of values for the surface conductivities of these materials.
