Systems that exhibit the extraordinary magnetoresistance (EMR) effect and other more disordered semiconductor-metal hybrid structures have been investigated numerically with the use of the finite element method (FEM). Initially, modelling focused on circular geometry EMR devices where a single metallic droplet is embedded concentrically into a larger semiconducting disk. The dependence of the magnetoresistance of such systems on the transverse magnetic field (0 5T) and filling factor (1/16 15/16) are reported and generally show a very good agreement with existing experimental data. The influence of the geometry of the conducting region of these EMR systems was then investigated. The EMR effect was found to be highly sensitive to the shape of the conducting region with a multi-branched geometry producing a four order of magnitude enhancement of the magnetoresistance over a circular geometry device of the same filling factor. Conformal mapping has previously been shown to transform a circular EMR device into an equivalent linear geometry. Such a linear EMR device has been modelled with the EMR mechanism clearly observed. The magnetoresistive response of a circular EMR device upon changes to: the mobility of the semiconducting region; the ratio of metal to semiconductor conductivity; and the introduction of a finite resistance at the semiconductor-metal interface, have also been investigated. In order for a large EMR effect to be observed the system requires: the semiconductor mobility to be large; the conductivity of the metal to be greater than two orders of magnitude larger than that of the semiconductor; and a very low interface resistance. This modelling procedure has been extended to include inhomogeneous semiconductor-metal hybrids with a more complex and disordered structure. Two models are presented, both based upon the random distribution of a small proportion of metal inside a semiconducting material. The resultant magnetoresistance in each case is found to have a quasi-linear dependence on magnetic field, similar to that observed in the silver chalcogenides.

During neural activity, action potentials travel down axons, generating effective charge current pulses, which are central in neuron-to-neuron communication. Consequently, said current pulses generate associated magnetic fields with amplitudes on the order of picotesla (pT) and femtotesla (fT) and durations of 10’s of ms. Magnetoencephalography (MEG) is a technique used to measure the cortical magnetic fields associated with neural activity. MEG limitations include the inability to detect signals from deeper regions of the brain, the need to house the equipment in special magnetically shielded rooms to cancel out environmental noise, and the use of superconducting magnets, requiring cryogenic temperatures, bringing opportunities for new magnetic sensors to overcome these limitations and to further advance neuroscience. An extraordinary magnetoresistance (EMR) tunable graphene magnetometer could potentially achieve this goal. Its advantages are linear response at room temperature (RT), sensitivity enhancement owing to combination of geometric and Hall effects, microscale size to place the sensor closer to the source or macroscale size for large source area, and noise and sensitivity tailoring. The magnetic sensitivity of EMR sensors is, among others, strongly dependent on the charge mobility of the sensing graphene layer. Mechanisms affecting the carrier mobility in graphene monolayers include interactions between the substrate and graphene, such as electron-phonon scattering, charge impurities, and surface roughness. The present work reviews and proposes a material set for increasing graphene mobility, thus providing a pathway towards pT and fT detection. The successful fabrication of large-size magnetic sensors employing CVD graphene is described, as well as the fabrication of trilayer magnetic sensors employing mechanical exfoliation of h-BN and graphene. The magneto-transport response of CVD graphene Hall bar and EMR magnetic sensors is compared to that obtained in equivalent trilayer devices. The sensor response characteristics are reported, and a determination is provided for key performance parameters such as current and voltage sensitivity and magnetic resolution. These parameters crucially depend on the material's intrinsic properties. The Hall cross magnetic sensor here reported has a magnetic sensitivity of ~ 600 nanotesla (nT). We find that the attained sensitivity of the devices here reported is limited by contaminants on the graphene surface, which negatively impact carrier mobility and carrier density, and by high contact resistance of ~2.7 kΩ µm at the metallic contacts. Reducing the contact resistance to < 150 Ω µm and eliminating surface contamination, as discussed in this work, paves the way towards pT and ultimately fT sensitivity using these novel magnetic sensors. Finite element modeling (FEM) is used to simulate the sensor response, which agrees with experimental data with an error of less than 3%. This enables the prediction and optimization of the magnetic sensor performance as a function of material parameters and fabrication changes. Predictive studies indicate that an EMR magnetic sensor could attain a sensitivity of 1.9 nT/√Hz employing graphene with carrier mobilities of 180,000 cm²/Vs, carrier densities of 1.3×10¹¹ cm^-2 and a device contact resistance of 150 Ω µm. This sensitivity increments to 443 pT/√Hz if the mobility is 245,000 cm²/Vs, carrier density is 1.6×10¹⁰ cm^-2, and a lower contact resistance of 30 Ω µm. Such devices could readily be deployed in wearable devices to detect biomagnetic signals originating from the human heart and skeletal muscles and for developing advanced human-machine interfaces.