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Vol. 30, No. 6 Journal of Semiconductors June 2009Effect of a step quantum well structure and an electric-field on the Rashba spin splitting∗Hao Yafei( ), Chen Yonghai( )†, Hao Guodong( ), and Wang Zhanguo( ) (Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China)Abstract: Spin splitting of conduction subbands in Al0.3 Ga0.7As/GaAs/Alx Ga1−x As/Al0.3 Ga0.7 As step quantum wells induced by interface and electric field related Rashba effects is investigated theoretically by the method of finite difference. The dependence of the spin splitting on the electric field and the well structure, which is controlled by the well width and the step width, is investigated in detail. Without an external electric field, the spin splitting is induced by an interface related Rashba term due to the built-in structure inversion asymmetry. Applying the external electric field to the step QW, the Rashba effect can be enhanced or weakened, depending on the well structure as well as the direction and the magnitude of the electric field. The spin splitting is mainly controlled by the interface related Rashba term under a negative and a stronger positive electric field, and the contribution of the electric field related Rashba term dominates in a small range of a weaker positive electric field. A method to determine the interface parameter is proposed. The results show that the step QWs might be used as spin switches.Key words: Rashba effect; step quantum wells; electric field; interfaceDOI: 10.1088/1674-492 6/30/6/062001 PACC: 7170E; 7320D1. IntroductionIt has been shown that the Rashba spin-orbit coupling can be controlled by a gate voltage, which offers the possibility of altering the symmetry of the quantum well (QW)[1−3]. Thisprovides an effective way to realize the so-called spin field ef- fect transistor[4, 5] and other spintronic devices[6, 7]. However,tric field, which is controlled by the gate voltage, to such a step QW may affect the SIA of the step QW. It has been re- ported that the introduction of an InP layer above the QW affects the spin-orbit interaction by the effect of the doping position[14]. In this paper, we will show the effect of the ex- ternal electric field and the structure of the step QW, weighedby the well width and step width, on the spin splitting of theit is proposed that the contribution of the potential jump atthe well barrier interfaces to the Rashba spin-orbit coupling isAl0.3Ga0.7 As/GaAs/Alx Ga1−xAs/Al0.3Ga0.7As step QW com-larger than that of the vertical electric field in the well, which can be varied by the gate voltage[8−10], and the spin splitting is underestimated if the interface contribution is neglected[11].In order to investigate the contribution of the band disconti- nuity to the Rashba spin splitting, many researchers focus on the asymmetrical QW with different barrier materials[12, 13]. However, the electron confinement is diminished in the asym- metrical QW compared with the symmetrical QW. In order to overcome the weakness, we focus our attention on the Al0.3 Ga0.7As/GaAs/Alx Ga1−x As/Al0.3 Ga0.7As step QW, whichprovides a good probe for the interface contribution to theposed of intrinsic semiconductor materials. Moreover, we willgive a method to determine the interface parameter, which is very important for the spin splitting of the asymmetrical struc- ture.2. TheoryFor the [001]-grown step QW, the Hamiltonian describ- ing the SIA contribution to the conduction subbands can be written as~2 2spin splitting. The step QW contains a built-in structure in- version asymmetry (SIA), which is introduced by insertingH = − 2m∗ ∇+ V0 + eF z + Hso , (1)the Alx Ga1−x As step into the Al0.3 Ga0.7 As/GaAs/Al0.3 Ga0.7 As symmetrical QW. The merit of the step QW is that it possesses an internal SIA, which induces a Rashba effect without any electric field or magnetic field as opposed to the case of the symmetrical QW, and the effect of the confining electrons is better than that of the asymmetrical QW. Applying an elec-where m∗ is the electron effective mass, V0 is the band offset,eF z is the potential induced by the external electric field, and Hso is the Rashba Hamiltonian containing the interface and electric field related Rashba terms, which can be written asHso = (αF + αI )(σxky − σy kx ), (2)∗ Project supported by the State Key Development Program for Basic Research of China (Nos. 2006CB921607, 2006CB604908) and theNational Natural Science Foundation of China (No. 60625402).† Corresponding author. Email: yhchen@Received 15 December 2008, revised manuscript received 16 January 2009 c 2009 Chinese Institute of Electronics062001-1J. Semicond. 30(6) Hao Yafei et al.where kx and ky are the wave vectors, σx and σy denote the spin Pauli ma。