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

TL;DR

This paper develops a unified semiclassical theory for spin-polarized electron transport in ferromagnet/semiconductor heterostructures, combining ballistic and diffusive mechanisms to better understand spin relaxation and transport interactions in spintronic devices.

Contribution

It introduces a comprehensive framework that unifies ballistic and diffusive transport, including spin relaxation, in semiconductor heterostructures, extending standard models to account for interface effects and electric fields.

Findings

Derived an integral equation for spin transport function.

Converted the integral equation into a generalized spin drift-diffusion equation.

Illustrated effects of transport mechanisms and electric fields on spin polarization.

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 framework for 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 values of the momentum and spin relaxation lengths. For field-driven transport in a homogeneous semiconductor, the integral equation can be converted 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 which illustrate the effects of transport mechanism and electric field.