Effects of Contact Placement and Sample Shape in the Measurement of Electrical Resistivity

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Abstract
The resistivity of a sample is given by ρ=VI−12πsF, where V is the voltage, I is the current, s is the voltage contact separation, and F is a correction factor appropriate to the sample geometry. Correction factors are found for the cases of parallelepiped samples with (1) nonequidistant point contacts symmetrically located on the top face, and (2) point voltage contacts symmetrically located on the top face and point current contacts centered on the end faces. In studies of these cases, curves are given for determining the geometries which give, between the voltage contacts, current densities directed parallel to the sample length. Although in the development it is assumed that the resistivity is homogeneous and isotropic and that there is no magnetic field present, a discussion is given on the applicability to anisotropic resistivity and low magnetic fields. Experimental verification is given.