A numerical analysis of various cross sheet resistor test structures

Abstract Various four-terminal cross sheet resistor test structures were analyzed to determine the effect of the contact arm width and length on the measured sheet resistance. A nine-point finite difference approximation to the Laplace equation was used with a six-resistor equivalent circuit to solve for the sheet resistance measurement error. The error indicates the difference between the true sheet resistance and the sheet resistance calculated from the van der Pauw formula. The analysis demonstrates that many novel designs are possible. In particular, the Greek-cross sheet resistor is a valid van der Pauw test structure if the arm length is greater than the arm width. This test structure is important in that it allows the accurate measurement of the sheet resistance of a very small region whose width is limited only by the fabrication technology.