Analytical expressions for the conductance noise measured with four circular contacts placed in a square array

摘要

In the ideal case, noise measurements with four contacts minimize the contribution of the contact interface. There is a need to characterize conductance noise and noise correction factors for the different geometries provided with four contacts, as already is the case for resistivity measurements with van der Pauw structures. Here, we calculate the noise correction factors for two geometries with a pair of sensors and a pair of current driver electrodes placed in a square array. The first geometry investigated is a very large film compared to the distance L between four circular electrodes, which are placed in a square array far away from the borders of the film. The second is a square-shaped conductive film with side length L and provided with four quarter-circle corner contacts with radius l. The effect of the conductance noise in the film can be observed between current free sensors in a four-point measurement or between current carrying drivers in a two-point measurement.