Micro-four-point probe Hall effect measurement method

We report a new microscale Hall effect measurement method for characterization of semiconductor thin films without need for conventional Hall effect geometries and metal contact pads. We derive the electrostatic potential resulting from current flow in a conductive filamentary sheet with insulating barriers and with a magnetic field applied normal to the plane of the sheet. Based on this potential, analytical expressions for the measured four-point resistance in presence of a magnetic field are derived for several simple sample geometries. We show how the sheet resistance and Hall effect contributions may be separated using dual configuration measurements. The method differs from conventional van der Pauw measurements since the probe pins are placed in the interior of the sample region, not just on the perimeter. We experimentally verify the method by micro-four-point probe measurements on ultrashallow junctions in silicon and germanium. On a cleaved silicon ultrashallow junction sample we determine carrier mobility, sheet carrier density, and sheet resistance from micro-four-point probe measurements under various experimental conditions, and show with these conditions reproducibility within less than 1.5%.