Spin diffusion and injection in semiconductor structures: Electric field effects

In semiconductor spintronic devices, the semiconductor is usually lightly doped and nondegenerate, and moderate electric fields can dominate the carrier motion. We recently derived a drift-diffusion equation for spin polarization in semiconductors by consistently taking into account electric-field effects and nondegenerate electron statistics and identified a high-field diffusive regime which has no analog in metals. Here spin injection from a ferromagnet (FM) into a nonmagnetic semiconductor (NS) is extensively studied by applying this spin drift-diffusion equation to several typical injection structures such as FM/NS, FM/NS/FM, and FM/NS/NS structures. We find that in the high-field regime spin injection from a ferromagnet into a semiconductor is enhanced by several orders of magnitude. For injection structures with interfacial barriers, the electric field further enhances spin injection considerably. In FM/NS/FM structures high electric fields destroy the symmetry between the two magnets at low fields, where both magnets are equally important for spin injection, and spin injection becomes determined by the magnet from which carriers flow into the semiconductor. The field-induced spin injection enhancement should also be insensitive to the presence of a highly doped nonmagnetic semiconductor $\left({\mathrm{NS}}^{+}\right)$ at the FM interface, thus ${\mathrm{F}\mathrm{M}/\mathrm{N}\mathrm{S}}^{+}/\mathrm{NS}$ structures should also manifest efficient spin injection at high fields. Furthermore, high fields substantially reduce the magnetoresistance observable in a recent experiment on spin injection from magnetic semiconductors.