Design Optimization toward Enhancing Response in Extraordinary Magnetoresistive Devices

Magnetic field sensing plays a crucial role in various modern applications, including neuroscience, magnetic nanoparticle-based drug delivery, and the characterization of nanoscale materials. Although highly sensitive techniques such as superconducting quantum interference devices exist, they require cryogenic temperatures, large equipment, and magnetically shielded environments. Extraordinary magnetoresistance (EMR), on the other hand, offers a room-temperature alternative whose magnetic field response primarily depends on its geometry. Since EMR is governed by classical current deflection, its behavior can be accurately studied using numerical simulations, and the dependence on its geometry provides ample design space for enhancing their performance. However, later experimental devices were unable to reproduce the very high MR values reported in the first EMR structures, and research interest has consequently declined. This thesis investigates the magnetic field response of concentric circular EMR devices through four numerical studies: the influence of device topography, the effect of local material properties on the contact layer, a comparison of embedded and top-contacted EMR devices, and the application of topology optimization (TO) to enhance magnetoresistance.

The impact of topography on EMR device performance was numerically examined using three-dimensional models, where we studied topographical variations within an embedded device in which the metal is side-contacted to the inner circumference of a semiconductor ring. We compared the performance of embedded devices against the top-contacted devices, where the metal is deposited on top of the semiconductor disk. In both studies, the metal-semiconductor contact layer was not included. For embedded structures, the metal thickness has a significant influence on the zero-field resistance, allowing for control of the magnetoresistance over several orders of magnitude. On the other hand, a thin sidewall region has little impact when the contact layer is neglected. When the embedded device was gradually transformed into a topcontacted configuration, both designs produced nearly identical magnetoresistance in the absence of specific contact resistivity. However, current streamlines and density maps indicate a significant difference in electrodynamics between these devices. In top-contacted devices, the metal thickness again sets the zero-field resistance and increases the magnetoresistance until it reaches a saturation regime when the metal thickness exceeds its radius. Comparison with the experimental results from the first EMR sensor showed that a 3D model with a metal thickness equal to 0.6 times the semiconductor thickness reproduced the measurements more accurately than a traditional 2D model, underscoring the importance of 3D modeling when devices have significant topography.

Secondly, the impact of specific contact resistivity was examined by explicitly modeling the contact layer sandwiched between the metal and semiconductor, and independently varying its mobility and carrier density. These results were compared to the device where the contact layer is modeled using a contact impedance boundary condition, which is an infinitesimally thin contact layer whose properties are independent of the magnetic field. Our study shows that the specific contact resistivity, ρ_c, is the primary parameter governing the behavior of EMR devices, largely independent of the precise mobility or carrier density within the contact layer. A value of ρ_c < 10⁻⁵,Ω · cm² is required for strong magnetic field response in EMR devices based on InSb-Au which confirmed previous published results. While a high semiconductor mobility is essential, high mobility within the contact layer is not necessary for achieving high magnetoresistance. These findings clarify how contact engineering and the product n_cμ_c influence the role of metal inclusions in EMR devices. Additionally, it confirms that the contact impedance boundary condition can be used to mimic the influence of the contact layer in numerical models.

Next, the magnetoresistance of top-contacted and embedded devices was evaluated across a wide range of specific contact resistivity (010,Ω · cm²) and device sizes (10⁻⁵10⁻¹ m). Specific contact resistivity has a substantial effect on embedded devices owing to their smaller contact area, which scales with device radius. In contrast, top-contacted devices benefit from a larger area that scales with radius squared, reducing the impact of specific contact resistivity. Increasing device size reduces the zero-field resistance and mitigates the impact of specific contact resistivity in both topologies, as a greater fraction of the current is diverted through the metal. We observed that for large device sizes (> 10⁻⁵ m), top-contacted devices perform better compared to embedded devices in the presence of significant specific contact resistivity. Current-density maps and transfer-length analysis provide clear physical insight into these trends, offering design guidance for device scaling under various contact layer properties.

Finally, TO was used to explore the design space of 2D and 3D EMR devices and enhance the magnetoresistance at 1 T. All 2D optimizations with different initial conditions converged to metal pathways linking the supply and voltage leads, along with fine interdigitated metal-semiconductor channels. These geometries consistently produced extremely high magnetoresistance, reaching about 1012 % at 1 T, which is over seven orders of magnitude higher than the structure reported in the first EMR device. The design space for the EMR device is highly non-convex, as minor geometric variations appeared across identical runs; however, the performance and core structural features remained essentially unchanged. Experiments confirmed considerable MR enhancements, with the best device exceeding 108 % at 1 T. Numerical simulations based on a one-band (single charge carrier) model accurately predicted the zero-field resistance but were unable to capture the high-field behavior. In contrast, a two-band (containing two types of charge carriers) model closely matched the measurements quite well. Further, the TO framework in 2D was extended to 3D using both the direct and general-extrusion methods. Both approaches recover the same key structural features and yield MR values comparable to those obtained in the 2D TO. However, the 3D-direct method is more computationally efficient. Moreover, the TO of top-contacted devices with a contact layer is possible only through 3D formulations. A preliminary comparison of top-contacted and embedded devices, topology-optimized using both the 3D-direct and general extrusion methods, is also provided against the 2D TO.

Together, these results provide a detailed understanding of how topography, contact layer properties, device topology, and geometric optimization govern the EMR effect, and they offer a clear framework for designing high-performance EMR devices and magnetometers.