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.
A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.