Spin-injection efficiency and magnetoresistance in a hybrid ferromagnetic–semiconductor trilayer with interfacial barriers

Abstract

We present a self-consistent model of spin transport in a ferromagnetic (FM)–semiconductor (SC)–FM trilayer structure with interfacial barriers at the FM–SC boundaries. The SC layer consists of a highly doped n²⁺ AlGaAs–GaAs 2DEG while the interfacial resistance is modeled as delta potential (δ) barriers. The self-consistent scheme combines a ballistic model of spin-dependent transmission across the δ-barriers, and a drift-diffusion model within the bulk of the trilayer. The interfacial resistance (R_I) values of the two junctions were found to be asymmetric despite the symmetry of the trilayer structure. Transport characteristics such as the asymmetry in R_I, spin-injection efficiency and magnetoresistance (MR) are calculated as a function of bulk conductivity σ_s and spin-diffusion length (SDL) within the SC layer. In general a large σ_s tends to improve all three characteristics, while a long SDL improves the MR ratio but reduces the spin-injection efficiency. These trends may be explained in terms of conductivity mismatch and spin accumulation either at the interfacial zones or within the bulk of the SC layer.

Introduction

Semiconductor (SC)-based spintronics which exploits the spin as well as the charge property of carriers, is a fast growing field of research. The long spin coherence of electrons in SC [1], coupled with the ability to control spin orientation by electrical means [2] has opened the possibility of realizing devices such as the Datta–Das spin field effect transistor [3] (spin-FET). A chief prerequisite of such devices is the ability to inject spin-polarized current into semiconductor materials, which are usually non-magnetic. Initial experimental efforts at spin-injection were not very successful with the resultant spin injection efficiency η of the order of 1% only [4], [5]. Furthermore, the signals from such a small spin polarization of the current could possibly be ascribed to other effects such as the local Hall effect in the vicinity of the ferromagnetic spin injector or detector [6], [7] although subsequent experiments by Hammar et al. [8] did account for this spurious local Hall effect. The reasons for such low values of spin-injection efficiencies have also been explained in terms of conductivity mismatch [9]. More recently, a much higher spin injection efficiency η exceeding 30% [10], [11] has been achieved for injection from a Fe contact into a AlGaAs–GaAs quantum well structure through a Schottky barrier. In addition, an appreciable spin-polarization value of 13% was obtained, albeit at a low temperature of 2 K, for injection from a Heusler alloy into a AlGaAs/GaAs light-emitting diode [12], which also involves a Schottky contact. The crucial element for these recent successes is the incorporation of interfacial barriers, e.g. tunnel or Schottky barriers between the FM and SC layers, to overcome the conductivity mismatch problem, as was theoretically proposed by Rashba [13].

In this paper we consider a FM–SC–FM trilayer structure with interfacial resistive (R_I) barriers at the SC–FM boundaries. The role of R_I in determining the overall charge and spin transport has been investigated in previous work [14]. However, the characteristics of the SC layer also play a prominent role, owing to the relatively large resistivity of the SC layer (about five orders of magnitude larger than that of the FM contacts). Thus, the main focus of this article is to investigate the effects of changing the bulk-SC conductivity and the spin-diffusion length of the SC region on the spin injection efficiency and overall magnetoresistance (MR) of a FM–SC–FM trilayer. In general, an increase in the conductivity and spin-diffusion length of the SC material improves the spin-injection efficiency and MR of the device by maintaining spin coherence, and reducing the conductivity-mismatch [9] problem, respectively. However, the presence of R_I complicates the analysis. For instance, a short SC spin-diffusion length enhances the spin-accumulation effect adjacent to the FM–SC interfaces, which can also improve the spin-injection efficiency. It is thus important to analyze the effects of varying conductivity as well as spin-diffusion lengths of the SC region on the spin transport characteristics of the device.

In our model, we determine the interfacial resistances via a self-consistent drift-diffusion and ballistic model. The diffusive part of the model is based on the spin-dependent drift-diffusion (DD) equation. The R_I values are evaluated by considering ballistic tunneling transmission across δ-function potential barriers at the FM–SC interfaces. The incorporation of interfacial δ-barriers makes our model similar to that of Heersche et al. [15]. But the latter assumes fully ballistic transport through the structure and is limited to a single junction. However in this paper, we consider a trilayer structure in which the SC layer thickness $w$ is assumed to be larger than the carrier mean free path (MFP), although it is comparable to the spin-diffusion length in the SC material. It is thus necessary to incorporate a diffusive model to model the charge and spin transport in the SC layer away from the interfacial zones. The trilayer material consists of a highly doped n²⁺ AlGaAs–GaAs 2DEG (SC) layer sandwiched between two Fe (FM) layers.

The δ-potential barriers at the two FM–SC interfaces are expressed as $U[\delta (x)+\delta (x-w)]$ with the barrier height U being spin-dependent, as was assumed by Yu and Flatte [16] and Smith and Silver [17]. The quantitative description of tunneling at the FM–SC interface is rather complicated because the transport properties are strongly dependent on the potential barrier height and thickness, and are highly sensitive to interfacial roughness and impurity states within the barriers. However, as a first approximation, we ignore any type of electron scattering within the barriers and assume purely ballistic transport through them.