Spin diffusion and injection in semiconductor structures:  Electric field effects

Abstract

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 driftdiffusion equation for spin polarization in the semiconductors by consistently taking into account electric-field effects and nondegenerate electron statistics and identified a high-field diffusive regime which has no analogue 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 locally 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 (NS + ) at the FM interface, thus FM/NS + /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.

Spin dynamics in semiconductors

“…Without the electric field, the spin injection length is the diffusion length L s . The applied electric field can significantly change the injection length by dragging or pulling the electron [928,929]: For a large downstream electric field, the electron spin injection is the distance that the electrons move with drift velocity within the spin lifetime time, L s (E) = L d ; for large upstream field, L s (E) = L 2 s /L d .…”

“…When a semiconductor is in contact with a spin polarization source at x = 0, B = 0 and the electric field is along the x-direction, the drift-diffusion model predicts spin accumulation with an exponential decay in the semiconductor S(x) = S 0 exp[−x/L s (E)], in which the electric-field-dependent spin injection length reads [904,928,929]…”

Diffusion models for spin transport derived from the spinor Boltzmann equation

“…In the twocomponent description, the electrons are considered to be of two types, namely, having spin up or down. Each type of electrons is described by the usual drift-diffusion equation with additional terms related to sources and relaxation of the electron spin polarization, see [26,27,18]. In this kind of model, the mechanism of spin relaxation (such the spin-orbit interaction for instance) is not specified.…”

“…Many theoretical models are used by the physical community for spin-polarized transport [17,18,20,22,23,25,26,27,28]. In microelectronics the drift-diffusion system is one of the most used model for modelling the transport of charged particles in semiconductors [14,15], Plasma [3], Gas Discharges [21], etc.…”

Spin injection and detection in lanthanum- and niobium-doped SrTiO3 using the Hanle technique

“…At positive DC bias (spin injection), the spin signal is higher than that for negative DC bias (spin extraction), indicating a higher spin accumulation in the former case. This behaviour is likely related to the bias dependence of the electronic structure and/or the bias dependence of the spin injection/detection efficiency 16 . The bias dependence of the spin lifetime for this same sample was studied at 10 K, as summarized in Fig.…”