RESISTIVITY DETERMINATION FROM SMALL CRYSTALLITES

We determine the resistivity of small micrometer-sized conductors with arbitrary shapes. It is shown that with n terminals attached to the s ample, there are n(n-1)/2 independent measurements of the resistance t hat can be made; from which the sample resistivity and the contact res istances can be extracted. An image of the sample is digitized and a f inite element analysis is used to determine the geometrical factors th at arise from the nonuniform current flow and hence control the resist ance 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 re sistivity and the contact resistances extracted. This technique is a p ractical example of an inverse problem.