On the magnetoresistance of finite semiconductors

We show in this work that the magnetoresistance in a weak magnetic field B under certain conditions has a linear dependence on the magnetic field B. We obtain new formulas for the quadratic and linear dependence of the magnetoresistance on the magnetic field in bounded semiconductors. The linear contribution to the magnetoresistance arises from the spatial dependence of the potential at the electrical contacts. Some fluctuation of physical characteristics at the contacting planes always exists in real experiments, and it leads to the spatial dependence of the potential at the contacts. We describe the inhomogeneity of the potentials at the contacting planes x = 0 and x = a accordingly by the functions φ⁰(z), φ^a(z). The spatial dependence of the contacting potentials can be determined through the magnetoresistance as a function of the magnetic field.