Spin polarized transport in 1D and 2D semiconductor heterostructures

The high electron mobility spin transistor comprises a 1D or 2D electron gas, obtained from III-V semiconductor heterostructure, with ferromagnetic source and drain contacts. The latter act respectively as a polarizer and as an analyzer for the spin of the electrons, and the gate potential is used to control the spin precession in the channel. After reviewing the main spin dephasing effects existing in III-V heterostructures, we present the model that we develop to investigate the spin polarized transport in the channel of a HEMT. The results obtained from this model show that in a 2D electron gas the spin polarization is randomized by the scattering events, which leads to non negligible loss of spin polarization. However, this spin relaxation vanishes if the width of the 2D-channel is sufficiently reduced, or if a 1D-channel is used. In these conditions, the gate-controlled spin rotation may yield a large negative transconductance effect. We discuss finally the spin-dependent injection/collection from ferromagnets. Introduction The magnetoelectronics is an emerging domain of research, based on a specific property of ferromagnetic contacts: they inject or collect electrons with a preferential spin orientation depending on their magnetic moment, leading so to "spin polarized" currents [1]. This property was first experimentally demonstrated in ferromagnet/insulator/superconductor tunnel junctions by the pioneering works of Tedrow and Meservey [2]. More recently, metallic structures exploiting this concept were developed. The giant magnetoresistances (GMR) [3], consisting of ferromagnetic layers separated by paramagnetic layers, are already used in industrial application as read heads in hard drives. The magnetic tunneling junctions (MTJ) [4], consisting of two ferromagnets separated by a thin insulating layer, seem promising structures for nonvolatile memory effect. Till now, studies concerning spin-polarized current in semiconductor/ferromagnet structures remain rare. Monsma et al. [5] have developed a bipolar hot carrier transistor with a GMR multilayer as base region, but this structure does not exploit any semiconductor property relative to spin. However, Datta and Das [6] have indeed proposed in 1990 a particular concept of High Electron Mobility Transistor (HEMT) which applies properties of ferromagnets and of semiconductor heterostructures relative to spin. This structure consists in a HEMT where usual highly doped source and drain regions are replaced by ferromagnetic contacts, as shown in Fig. 1. These contacts should act as spin polarizer and analyzer. The new concept appearing in this device is the "magnetic" control of the drain current by the gate voltage, in addition to the classical field effect control. The existence of a gate-controlled spin-orbit coupling term in asymmetric quantum wells makes actually feasible the control of the electron spin precession in the channel layer of a HEMT. This term, depending on the perpendicular electric field at the HEMT-heterointerface, is often denoted as the Rashba mechanism [7]. So, one obtain the principle of a "spin-HEMT": the source contact imposes the spin orientation of electrons injected in the HEMT-channel, this spin orientation is modified by the gate voltage during the electrons motion in the channel, and the UFPS10, Vilnius, August 31-Sept. 2 1998, Materials Science Forum 297-298, 205-212 (1999) 2 transmitted current at drain depends on the comparison of the spin orientation of electrons reaching this contact with the magnetic moment orientation of ferromagnetic drain. The possibility to develop magnetoelectronics in modulation-doped semiconductor heterostructures forms the subject of this paper. After Datta and Das, the magnetic control of drain current is not efficient if the electrons in the channel form a two dimensional electron gas (2DEG) as usual in a HEMT-channel, and the spin orientation control would be efficient only if the electrons are confined also laterally, in a one dimensional electron gas (1DEG). We will thus examine the control of the spin precession in both cases of quantum confinement. Our paper is organized as follows. In Sec. 1, we review the spin dephasing effects appearing in III-V heterostructures. In Sec. 2, we describe our approach to the spin polarized transport in 1D and 2D heterostructures. The results obtained from this model are presented in Sec. 3. Finally, we discuss in Sec. 4 the spin dependent injection/collection with ferromagnetic contacts. 1. Spin dephasing effects in III-V heterostructures To study the concept of the gate-controlled spin precession, we have developed a model for spin-polarized transport in III-V heterostructures. To determine how effects acting on spin orientation have to be treated, we first have to review the main effects of this type existing in III-V heterostructures: (i) The Rashba interaction is a spin-orbit coupling that arises from the strong asymmetry of the conduction band in a modulation-doped heterostructure [7]; (ii) The spin-orbit term due to the lack of inversion symmetry of the zinc-blende crystal, existing in bulk, first described by Dresselhaus [8]; (iii) The spin-orbit interaction with perturbing potential related to ionized impurities or to lattice vibrations, usually called Elliott-Yafet (EY) mechanism [9,10]. In bulk p-type III-V semiconductor, the exchange interaction between electrons and holes, usually called Bir-Aronov-Pikus (BAP) mechanism [9,10], appears also as a possible spin dephasing effect. This effect is only efficient in the case of high concentration of holes. In the conduction layer of a n-channel HEMT, BAP mechanism seems clearly negligible. Two categories of spin dephasing mechanisms are usually distinguished: interaction leading to instantaneous spin-flip events, and slow spin precession process. If the spin rotation angle after a time duration close to momentum relaxation time τp is very large, it is possible to consider that spin orientation changes instantaneously. A spin-flip probability deduced from Fermi golden rule is then associated to the process. But if spin rotation frequency is comparable to or less than 1/τp, spin-flip time can not be neglected in comparison with free-flight duration. In this case, one considers that the electron spin is submitted to a pseudo-magnetic field B, so its orientation changes continuously during free-flights with the precession vector Ω=−γB, where γ is the electron gyromagnetic factor. The EY and BAP mechanisms [9,10] lead to instantaneous spin-flip events, the Dresselhaus term [9-11] and the Rashba term [12,13] correspond to slow spin precession. The Rashba and Dresselhaus terms lift spin degeneracy in modulation-doped III-V heterostructures. So, the energy subbands in the quantum well formed at heterointerface are spin splitted at zero magnetic field. Comparison between respective influences of Dresselhaus and Rashba terms has been a very debated subject. The measurement of the spin splitting is possible indeed by some ways, as electron spin resonance [14], magneto-conductance measurements [12,15], Raman scattering [16], Shubnikov-de Haas effect [17,18]. The theoretical analysis of these experimental data has been very controversial [7,15,16,19,20]. However, recent theoretical studies [21], in accordance with Raman scattering experimental data [16], proves Rashba term is the most important spin splitting term in AlGaAs/GaAs heterostructures. Furthermore, Rashba term is expected to be dominant in narrower bandgap semiconductors [19]. Recently, two research teams [17,18] have indeed experimentally demonstrated the possibility to control the strength of the Rashba spin-orbit coupling in gate-controlled In0.53Ga0.47As/In0.52Al0.48As and In0.53Ga0.47As/In0.77Ga0.23As/InP heterostructures. UFPS10, Vilnius, August 31-Sept. 2 1998, Materials Science Forum 297-298, 205-212 (1999) 3 The spin relaxation time τsEY corresponding to EY mechanism is approximately given by [9,10]