Abstract
We determine the resistivity of small micrometer-sized conductors with arbitrary shapes. It is shown that with $n$ terminals attached to the sample, there are $n(n\ensuremath{-}1)/2$ independent measurements of the resistance that can be made; from which the sample resistivity and the contact resistances can be extracted. An image of the sample is digitized and a finite element analysis is used to determine the geometrical factors that arise from the nonuniform current flow and hence control the resistance measurements. It is shown that all the elements of the resistance matrix for the sample are generated from the diagonal elements alone for an Ohmic sample, which provide a useful check of the experimental resistance measurements. To illustrate this approach, micrometer-sized diamond crystallites with four terminals were used, and the sample resistivity and the contact resistances extracted. This technique is a practical example of an inverse problem.
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