Conductance noise investigations with four arbitrarily shaped and placed electrodes

A general relation is derived for the spectral noise density of the voltage between two arbitrarily shaped and placed sensor electrodes on a conductor, when a constant current or voltage is applied to another pair of arbitrarily shaped and placed driver electrodes. The general relation is based on the sensitivity calculation in linear electrical networks. The relation is elaborated for conductivity fluctuations due to 1/f noise by using empirical 1/f noise relations. The influence of spot radii of the sensor electrodes on the noise is demonstrated. The theoretical results for 2 and 3-dimensional conductors are in agreement with our experimental results for carbon resistance sheets and on silicon and germanium in the resistivity range of 1Ωcm to 400Ωcm. The possibility of using the four-point probe for measuring the fluctuations in the resistivity has been demonstrated.