Koon, Daniel W.5; Wang, Fei6; Petersen, Dirch Hjorth1; Hansen, Ole3
1 Department of Micro- and Nanotechnology, Technical University of Denmark2 Nanointegration, Department of Micro- and Nanotechnology, Technical University of Denmark3 Experimental Surface and Nanomaterials Physics, Department of Physics, Technical University of Denmark4 Silicon Microtechnology, Department of Micro- and Nanotechnology, Technical University of Denmark5 St. Lawrence University6 South University of Science and Technology of China
Finite-field, intensity, and area corrections
We derive exact, analytic expressions for the sensitivity of sheet resistance and Hall sheet resistance measurements to local inhomogeneities for the cases of nonzero magnetic fields, strong perturbations, and perturbations over a finite area, extending our earlier results on weak perturbations. We express these sensitivities for conductance tensor components and for other charge transport quantities. Both resistive and Hall sensitivities, for a van der Pauw specimen in a finite magnetic field, are a superposition of the zero-field sensitivities to both sheet resistance and Hall sheet resistance. Strong perturbations produce a nonlinear correction term that depends on the strength of the inhomogeneity. Solution of the specific case of a finite-sized circular inhomogeneity coaxial with a circular specimen suggests a first-order correction for the general case. Our results are confirmed by computer simulations on both a linear four-point probe array on a large circular disc and a van der Pauw square geometry. Furthermore, the results also agree well with Náhlík et al. published experimental results for physical holes in a circular copper foil disc.
Journal of Applied Physics, 2014, Vol 116, Issue 13