Extraordinary magnetoresistance in two and three dimensions: Geometrical optimization

The extraordinary magnetoresistance (EMR) in metal-semiconductor hybrid structures was first demonstrated using a van der Pauw configuration for a circular semiconductor wafer with a concentric metallic inclusion in it. This effect depends on the orbital motion of carriers in an external magnetic field, and the remarkably high magnetoresistance response observed suggests that the geometry of the metallic inclusion can be optimized to further significantly enhance the EMR. Here, we consider the theory and simulations to achieve this goal by comparing both two-dimensional (2D) and three-dimensional (3D) structures in an external magnetic field to evaluate the EMR in them. New results for 3D structures are presented to show the feasibility of such modeling. Examples of structures that are compatible with present day technological capabilities are given together with their expected responses in terms of EMR. For a 10 μm 2D square structure with a square metallic inclusion, we find an MR up to 107 percent for ...