Sensor Calibration of Planar Four-Contact Devices with up to Two Extended Contacts

This paper reports on a novel method for the calibration of planar four-contact sensors making it possible to extract the sheet resistance R_sq of their conducting layer with minimal effort. We present extensions of van der Pauw´s method to determine R_sq holding for arbitrarily shaped four-terminal devices with one and two extended contacts. This is achieved by performing three and four electrical resistance measurements, respectively, on these devices. The results are obtained using the method of conformal mapping in combination with the method of images. Using finite-element analysis, our findings were verified to hold with a relative accuracy of better than 0.055%. Experimental tests with differently shaped structures corroborate the theoretical results.