Spin-polarized electron transport in ferromagnet/semiconductor heterostructures: Unification of ballistic and diffusive transport

Abstract

A theory of spin-polarized electron transport in ferromagnet/semiconductor heterostructures, based on a unified semiclassical description of ballistic and diffusive transport in semiconductor structures, is developed. The aim is to provide a comprehensive framework for systematically studying the interplay of spin relaxation and transport mechanism in spintronic devices. A key element of the unified description of transport inside a (nondegenerate) semiconductor is the thermoballistic current consisting of electrons which move ballistically in the electric field arising from internal and external electrostatic potentials, and which are thermalized at randomly distributed equilibration points. The ballistic component in the unified description gives rise to discontinuities in the chemical potential at the boundaries of the semiconductor, which are related to the Sharvin interface conductance. By allowing spin relaxation to occur during the ballistic motion between the equilibration points, a thermoballistic spin-polarized current and density are constructed in terms of a spin transport function. An integral equation for this function is derived for arbitrary profile of the electrostatic potential and for arbitrary values of the momentum and spin relaxation lengths. Detailed consideration is given to field-driven spin-polarized transport in a homogeneous semiconductor. An approximation is introduced which allows one to convert the integral equation into a second-order differential equation that generalizes the standard spin drift-diffusion equation. The spin polarization in ferromagnet/semiconductor heterostructures is obtained by invoking continuity of the current spin polarization and matching the spin-resolved chemical potentials on the ferromagnet sides of the interfaces. Allowance is made for spin-selective interface resistances. Examples are considered that illustrate the effects of transport mechanism and electric field.