ABSTRACT
The magnetic eld is indispensable in the characterization and performance evaluation of semiconductor devices. Magnetoresistance (MR) is the relative change Δρ/ρo in resistivity ρ from zero-eld resistivity ρo when an external magnetic eld is applied to them. In ordinary magnetoresistivity (OMR), the effect is rather small and can be classically described as a result of the force acting on conducting electrons in the magnetic and electric eld. A 3D sample can be converted into a 1D conguration when the magnetic eld is in the quantum domain. Unfortunately, for transverse conguration with the electric eld perpendicular to the applied magnetic eld, the traditional framework based on FD statistics and Boltzmann transport equation (BTE) is of limited use and density matrix takes on an increasing importance [1]. A quantum-mechanical theory using a density matrix for electrical conductivity in the presence of a magnetic eld is described. The conventional methods using the BTE are not satisfactory because the magnetic eld introduces a curvature in the free path of an electron. The expectation value of the current density and the components of the conductivity tensor in a magnetic eld are obtained. The advantages of the density matrix in electric transport problems with a magnetic eld are discussed.
