Surface Conductivity of Si(100) and Ge(100) Surfaces Determined from Four-Point Transport Measurements Using an Analytical N-Layer Conductance Model

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.