Extraordinary magnetoresistance in two and three dimensions: Geometrical optimization

Abstract

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 an applied magnetic field of 1 T. In 3D, for a 10 μm cube with a 5 μm centered metallic inclusion, we obtain an MR of ∼104 percent, which is comparable with the 2D structure of equivalent dimensions. The results presented here for specific geometries are scalable to smaller dimensions down to the onset of ballistic effects in the transport. The present calculations open up the possibility of 3D magnetic field sensors capable of determining the magnitude and also direction of the magnetic field once a full characterization of the sensor response is performed.