Electrical conductance sensitivity functions for square and circular cloverleaf van der Pauw geometries

We have undertaken the first systematic computational and experimental study of the sensitivity of charge transport measurement to local physical defects for van der Pauw circular and square cloverleafs with rounded internal corners and unclovered geometries, using copper-foil specimens. Cloverleafs with rounded internal corners are in common use and reduce sampling of the material near their boundaries, an advantage over sharp corners. We have defined two parameters for these cloverleafs, one of which, the 'admittance', is the best predictor of the sensitivity at the center of these specimens, with this sensitivity depending only weakly on the central 'core' size when its diameter is less than about 60% of the specimen's lateral size. Resistive measurement errors in all four geometries are linear in areas for errors up to about 50% in sheet resistance, and superlinear above. An ASTM-based 'standard' cloverleaf geometry, in which the central core diameter of the specimen is 1/5 the overall length and the slit widths are 1/10 the overall length, narrows the effective area sampled by the resistive measurement by a factor of about 16 × in the small-hole limit and over 40 × for larger holes, relative to unclovered goemetries, whether square or circular, with a smooth transition in these numbers for geometries intermediate between the standard cloverleaf and unclovered specimens. We believe that this work will allow materials scientists to better estimate the impact of factors such as the uniformity of film thickness and of material purity on their measurements, and allow sensor designers to better choose an optimal specimen geometry.