Topology-optimized Metal-Semiconductor Hybrid Structures to obtain Optimal Extraordinary Magentoresistance

Semiconductor wafer with metallic inclusions generates extraordinary magnetoresistance (EMR) response [1]. This effect has found applications in high sensitivity magnetic sensors, and smaller magnetic read heads. Since its inception, efforts have been made to increase magnetoresistance through different choices of materials, by altering location of contacts, filling factor, and shape of the device. However, a systemic study to optimize topology of the metallic inclusions has not been considered in the literature. Here, we employ a topology optimization scheme based on the level set function. For evolution of the level set curve, topological derivative is used as the sensitivity term in the Hamilton-Jacobi equation. In contrast to conventional homogenization based methods, this optimization scheme will not produce gray region in the metal-semiconductor boundary. We are also able to control the complexity of the structure to design realistic geometries for fabrication of the physical prototype. The optimized geometry is robust and independent of the initial configuration. When combined with material optimization, this algorithm manifests a potential for significant improvements in EMR technology.
[1] Moussa et al., Phys. Rev. B 64, 184410, (2001).