Theory of spin-polarized transport in ferromagnet–semiconductor structures: Unified description of ballistic and diffusive transport

A theory of spin-polarized electron transport in ferromagnet–semiconductor heterostructures, based on a unified semiclassical description of ballistic and diffusive transport in semiconductors, is outlined. The aim is to provide a framework for studying the interplay of spin relaxation and transport mechanism in spintronic devices. Transport inside the (nondegenerate) semiconductor is described in terms of a thermoballistic current, in which electrons move ballistically in the electric field arising from internal and external electrostatic potentials, and are thermalized at randomly distributed equilibration points. Spin relaxation is allowed to take place during the ballistic motion. For arbitrary potential profile and arbitrary values of the momentum and spin relaxation lengths, an integral equation for a spin transport function determining the spin polarization in the semiconductor is derived. For field-driven transport in a homogeneous semiconductor, the integral equation can be converted into a second-order differential equation that generalizes the spin drift-diffusion equation. The spin polarization in ferromagnet–semiconductor structures is obtained by matching the spin-resolved chemical potentials at the interfaces, with allowance for spin-selective interface resistances. Illustrative examples are considered.