Tunneling time of spin-polarized electrons in ferromagnet/insulator (semiconductor) double junctions under an applied electric field

Abstract

Based on the group velocity concept and the two-band model, we investigated tunneling properties of spin-polarized electrons traversing ferromagnetic/insulator (semiconductor) double junctions under the influence of an external electric field. The tunneling time and the transmission coefficient, as well as the spin polarization, were calculated and examined. Effects of the electric field and quantum size are also considered. The results indicate that the tunneling time strongly depends on the spin orientation of tunneling electrons. In a wide range of incident energy, spin-down electrons spend a longer time tunneling through the structure than spin-up ones, and the difference of the tunneling time Δτ between electrons with opposite spin orientation is very sensitive to the incident energy in the lower energy region. Moreover, the variation of Δτ with the increasing of the incident energy shows pronounced oscillations for certain applied bias and structural size. The results also indicate that spin polarization shows frequent wide-range oscillations and its magnitude decays slowly with the increasing of the incident energy, which reveal that the spin polarization in ferromagnetic/insulator (semiconductor) junctions possesses quite different properties from those exhibited in semiconductor electric-barrier or magnetic-barrier structures as well as semiconductor/semimagnetic semiconductor hybrid heterostructures.