| Recently, magnetoresistance (MR) effects have been widely concerned due to their significant values in theoretical studies and potential values in commercial applications. MR effect refers to remarkable variation of resistivity of materials at applied magnetic fields and it exists in various artificial or natural materials, such as artificial magnetic multi-layer films or granular composites, in which the MR effects are based on the spin-polarized scattering or spin-polarized tunneling mechanisms. Conventionally, MR effects mentioned above are called giant MR or tunneling MR. The alternative are doped pervoskite manganites in which MR is observed accompanied by a transition from a high temperature paramagnetic insulator to a low-temperature ferromagnetic metal at certain doped proportion. Near the critical point of the phase transition, resistivity of these materials is sensitive to the applied magnetic fields and the remarkable MR effects are observed during this process, which is the so-called colossal MR. The resistivity of the materials as mentioned above decreases with the increase of the applied magnetic fields. And the effects is called as "negative" MR effects and the MR is usually saturated at certain magnetic fields. In contrary, there are large positive MR effects observed in inhomogeneous nonmagnetic semiconductors and it was found that the resistance of the material increases notably with the increasement of the applied magnetic fields. This MR effect is called extraordinary effect (EMR). And this effect is different from the conventional MR effects and it is hardly explained by conventional magnetotransport theories. The magnetic sensors based on this effect have the advantages of low noise, small size and the developed techniques. Furthermore, they also have the advantages of good stability, high-degree precision and low-power expenditure. And they can be utilized both in steady-current and pulse sensors. Therefore, the EMR effect found in nonmagnetic field would lead to breakthrough in size of the devices, the restore density and the scope of the application.The magnetotransport properties of nonmagnetic semiconductors in different inhomogeneous structures are studied by theoretical analysis in this paper. The macroscopic MR effects are caused by the inhomogeneity of the materials where the components are nonmagnetic and they are determined by the structures of the current paths caused by the inhomogeneity. On one hand, from the microscopic level, we know that the basic mechanism in nonmagnetic semiconductor is the Hall effect, i.e. the applied magnetic fields influence magnetoresitance through acting on non-diagonal elements of the tensor of conductance. On the other hand, the relevant studies of experiments and theories have already exhibited that there is close relationship between EMR and the inhomogeneity of the materials. With the high degree of the regularity of the inhomogeneous materials, we can obtain the relationship between magnetotransport and inhomogeneity through calculating the equation of electromagnetism rigorously. For the disorder inhomogeneous nonmagnetic semiconductors, we treat them by adopting the effective-medium approximation (EMA) in tensional forms. EMA is an important method for studying the magnetotansport behavior of the inhomogeneous systems and it is often adopted for analyzing the influence on the magnetotransport of the inhomogeneity microscopically. However, the previous studies adopting EMA focused mainly on the situation of strong magnetic fields or the disorder of the mobility of carriers, i.e. the disorder of the Hall coefficient. Our theoretical work focus on the system that not only has the disorder of the mobility of carriers, but also the resistivity of carriers without the applied magnetic fields. And we obtain the extraordinary magnetotransport behaviors in the system in which the the conductivity mismatch among components is markable. Our main work and results can be summaried as follows.First, through setting the proper boundary conditions and adopting the analytical results of the electromagnetism equation, we obtain the relationship between voltage and disorder distribution of the system in semiconductor-metal with hybrid structure. And we obtain the global MR effects of the system consequently. We introduce three parameters which describe inhomogeneities of geometry, Hall coefficient and Ohm resistance respectively and we also consider their influence on the magnetotransport behaviors. As a result, these parameters have great impact on magnetotransport of the hybrid structure simultaneously. With the prerequisite condition that the coexistence of sharp contrast of mobility of the components and the component conductivities, the current paths in the system varies obviously with the applied magnetic fields. When the applied magnetic field is strong enough, the resistance increase sharply with the increase of the metal proportion. And the resistance would not decrease only if the metal proportion of the different phase is nearly 100%. Accordingly, MR of the material has maximum with introducing metal phase and the position and width of the peak are mediated by magnetic fields obviously. These results are consistent with the those observed in the experiments on the hybrid structures mentioned above. Further calculation shows that the signs of MR changed in the proper range of the mobility ratio and the conductivity ratio. The phenomenon is also been observed in other semiconductor composites but it has never been explained exquisitely. Our calculation results can serve as a starting point in studies of these inverse MR effetcs and they also offer an insight into the basic pictures of the magnetotransport phenomenoa in the hybrid structures composed by different materials.Secondly, considering the disorder distribution of the component mobility and the mismatch among conductivities, we construct two-component disorder conductance system and adopt conductivity tensors for describing the Hall effect. Then we calculate transverse magnetoresitance (TMR) (the orientation of the electric field is perpendicular to applied magnetic fields) and longitudinal magnetoresistance.(LMR)(the orientation of the electrical field is parallel to the applied magnetic fields). The results show that the MR effects not only depend on the disorder degree of mobility of carriers but also on resistivity of the components without applied magnetic fields. We focus mainly on the situation in which the mismatch of the resistivity under zero-magnetic field is remarkable. For the inhomogeneous disorder system, when the parameters of system (e.g. proportion of each component) reach a critical value, geometric percolation will emerge in the system, i.e. one of the component configuration changes from disconnection to connection. And the very value is called "percolation value" correspondently. The current tends to congregate in the component which has good conductance as the disparity among the components is large enough. Therefore, the macroscopic magnetotransport behaviors will change obviously at certain value of the component density and electrical percolation will take place in metal-insulator composites. The distribution of current paths without the magnetic fields influence the magnetotransport directly in the materials of nonmagnetic semiconductors. From our calculations, it is found that the number of the MR peaks evolves from one to two and the behavior of the magnetotransport becomes more complicated. Simultaneously, at the orientation parallel to the magnetic fields, the LMR emerges in a certain variation range of the component proportion. And these extraordinary MR effects are closely related to the percolation configuration. Although the microscopic mechanism of the phenomenon cannot be obtained by the EMA, it is clear that the behavior of TMR is related to the formation of the percolation path.The above extraordinary MR effects observed in inhomogeneous nonmagnetic semiconductos will extend the scopes of the application of the magnetoresistance devices. For instance, the non-saturating linear MR observed in doped nonmagnetic semiconductors makes magnetic field sensors based on EMR effects work in extremely strong magnetic fields. What'more, because EMR is determined mainly by the disorder distribution in mescopic range, the negative influence from environments such as temperature is weaker. Therefore, it is helpful to design the devices with more controllable qualities and better stability. |
