Beyond van der Pauw: Sheet resistance determination from arbitrarily shaped planar four-terminal devices with extended contacts

An extension of van der Pauw's method to determine the sheet resistance R
_sq
from arbitrarily shaped devices with four peripheral contacts of any size is presented. Extracting R
_sq
requires the measurement of six electrical resistances on these devices and the simultaneous solution of a system of six algebraic equations. The results are obtained using the method of conformal mapping in combination with the method of images. The computational effort to extract R
_sq
is modest. Using finite-element analysis, our findings were verified within a relative accuracy of better than 0.1%. Experimental tests with differently shaped structures are fully consistent with the novel theory.