⇦Chinese Physics Letters, 2019, Vol. 36, No. 7, Article code 077201 Spin Transport under In-plane Electric Fields with Different Orientations in Undoped InGaAs/AlGaAs Multiple Quantum Wells * Xiao-di Xue (薛小帝)1,2, Yu Liu (刘雨)2,3, Lai-pan Zhu (朱来攀)2,4, Wei Huang (黄威)2,5, Yang Zhang (张洋)2,3, Xiao-lin Zeng (曾晓琳)2,3, Jing Wu (吴静)2,3, Bo Xu (徐波)2, Zhan-guo Wang (王占国)2, Yong-hai Chen (陈涌海)2,3**, Wei-feng Zhang (张伟风)1** Affiliations 1Henan Key Laboratory of Photovoltaic Materials, Henan University, Kaifeng 475004 2Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing Key Laboratory of Low Dimensional Semiconductor Materials and Devices, Beijing 100083 3Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049 4Beijing Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 100083 5Science and Technology on Monolithic Integrated Circuits and Modules Laboratory, Nanjing Electronic Devices Institute, Nanjing 210016 Received 22 February 2019, online 20 June 2019 *Supported by the National Basic Research Program of China under Grant No 2015CB921503, the National Natural Science Foundation of China under Grant Nos 61474114, 11574302, 61627822 and 11704032, and the National Key Research and Development Program of China under Grant Nos 2018YFA0209103, 2016YFB0402303 and 2016YFB0400101.
**Corresponding author. Email: yhchen@semi.ac.cn; wfzhang@henu.edu.cn Citation Text: Xue X D, Liu Y, Zhu L P, Huang W and Zhang Y et al 2019 Chin. Phys. Lett. 36 077201    Abstract The spin-polarized photocurrent is used to study the in-plane electric field dependent spin transport in undoped InGaAs/AlGaAs multiple quantum wells. In the temperature range of 77–297 K, the spin-polarized photocurrent shows an anisotropic spin transport under different oriented in-plane electric fields. We ascribe this characteristic to two dominant mechanisms: the hot phonon effect and the Rashba spin-orbit effect which is influenced by the in-plane electric fields with different orientations. The formulas are proposed to fit our experiments, suggesting a guide of potential applications and devices. DOI:10.1088/0256-307X/36/7/077201 PACS:72.25.Dc, 72.40.+w, 72.25.Fe © 2019 Chinese Physics Society Article Text Spin manipulation schemes that do not require an external magnetic field are attractive for integration into existing semiconductor technologies.[1] One promising approach to nonmagnetic spin control is to exploit the Rashba effect through the spin-orbit interaction by electric fields.[2] Compared with vertical electric fields, the in-plane electric fields are more suitable for integrating into spintronic devices. Most of the previous studies have focused on the role of the in-plane electric fields only as the driving force of the drifting motion. With the deepening of research in the past few years, a variety of the phenomena[3–7] and novel spintronics concepts[8–12] are found to be related to the in-plane electric fields. Especially, the influence of in-plane electric fields on spin dynamics appears in various forms. For example, a spin helix with a special symmetry is achieved under a balanced Rashba and Dresselhaus spin-orbit interaction condition.[13,14] Thus, understanding how the different oriented in-plane electric fields affect the manipulation and transport of spins is important. Recently, the spin-polarized photocurrent has been proved to be an effective way to investigate how the electric fields work on the manipulation and transport of spins.[15,16] As a result of SOI induced $k$-linear band splitting and optical selection rules, the spin-polarized photocurrent is induced by an unbalanced occupation in the momentum space of carriers excited by circularly polarized light.[17] There are two kinds of origin for the $k$-linear terms corresponding to different sources of inversion asymmetric which will lead to the Dresselhaus and the Rashba spin-orbit terms in the Hamiltonian respectively. Different from the bulk inversion asymmetry (BIA) introduced by the intrinsic inversion asymmetry of the zinc-blende crystal structure, the structure inversion asymmetry (SIA) results from the asymmetry of heterostructures including the effect of built-in or external applied electric fields.[18–20] As a result, the spin-polarized photocurrent can intuitively show the influence of an electric field on the manipulation and transport of spins. In this Letter, we investigate the photocurrent excited by the circularly polarized light in undoped In$_{0.15}$Ga$_{0.85}$As/Al$_{0.3}$Ga$_{0.7}$As multiple quantum wells (MQWs). We study the photocurrent as functions of the incident angle and the azimuth angle, indicating that there exists an anisotropic in-plane spin splitting in two-dimensional electron gas (2DEG). Furthermore, the photocurrent helicity asymmetry under different oriented in-plane electric fields shows a strong anisotropy, and the formulas are proposed to fit our experiments. We interpret the anisotropic behaviors as a consequence of different dependence of the hot phonon effect and the Rashba effect under different oriented in-plane electric fields. A theoretical model is built by considering the effect of in-plane electric fields on the hot phonon effect and the Rashba effect, which fits well with our experiments. The samples studied here include undoped In$_{0.15}$Ga$_{0.85}$As/Al$_{0.3}$Ga$_{0.7}$As MQWs grown by molecular beam epitaxy. A 200-nm buffer layer was initially deposited on a (001) Si-GaAs substrate, followed by ten periods of 100 Å-In$_{0.15}$Ga$_{0.85}$As/100 Å-Al$_{0.3}$Ga$_{0.7}$As quantum wells. Then, a 500 Å Al$_{0.3}$Ga$_{0.7}$As layer and a 100 Å GaAs cap layer were deposited. Four ohmic electrodes were made along $X$ and $Y$ directions respectively, with indium deposited and annealed at about 420$^{\circ}\!$C in nitrogen atmosphere. The geometry is shown in Fig. 1.
cpl-36-7-077201-fig1.png
Fig. 1. The simple geometry of the experiment and the structure of the sample. The photocurrent is measured along the $Y$-direction. Note that different oriented in-plane electric fields are applied in sequence.
cpl-36-7-077201-fig2.png
Fig. 2. (a) Phase angle $\varphi$ dependence of photocurrent in (001)-grown In$_{0.15}$Ga$_{0.85}$As/Al$_{0.3}$Ga$_{0.7}$As MQWs normalized by the laser output $P$ of 250 mW at 970 nm. The photocurrent is measured at room temperature with the azimuth and incident angles of 0$^{\circ}$ and 30$^{\circ}$ (as shown in Fig. 1). The squares are the experimental data, and the solid line is the fit using Eq. (1). The dotted and dashed lines represent the circular photogalvanic current obtained by the fitting. (b) Incident angle $\theta_{0}$ dependence of the photocurrent helicity asymmetry at room temperature. The lines are the fitting results according to Eqs. (2) and (3). (c) Azimuth angle $\beta$ dependence of the photocurrent helicity asymmetry at room temperature.
For the spin-polarized photocurrent measurement, the sample is studied at different temperatures by a liquid-nitrogen cryostat which allows variation of the temperature from 77 to 297 K. A mode-locked Ti:sapphire laser with a repetition rate of 80 MHz and a pulse width of 140 fs serves as the excitation source, and it can excite electrons for the first valence subband of heavy holes to the first conduction subband from 77 to 297 K. A polarizer and a rotative quarter-wave plate are used to generate the linearly or circularly polarized light. The photocurrent is first amplified by a current pre-amplifier and then collected by a lock-in amplifier with the reference frequency of 220 Hz. The photocurrent is measured along the $Y$-direction, and a voltage source is used to apply electric fields in different orientations. Figure 2(a) shows the photocurrent $J$ as a function of phase angle $\varphi$. The photocurrent is measured at room temperature with the azimuth and incident angles of 0$^{\circ}$ and 30$^{\circ}$, respectively. The photogalvanic current consists of two components with different periodicities, which can be expressed as[17,21] $$\begin{align} J=J_{\rm C} \sin({2\varphi})+J_{\rm L} \sin({2\varphi})\cos({2\varphi})+J_{0},~~ \tag {1} \end{align} $$ where $J_{\rm C}$ and $J_{\rm L}$ denote the amplitudes of circular photogalvanic and linear photogalvanic currents, and $J_{0}$ is the background current due to the photovoltaic and Dember effect. Using Eq. (1) to fit the photogalvanic current obtained by experiments, one can obtain the circular photogalvanic current, as shown in Fig. 2(a). We define the photocurrent helicity asymmetry as $J_{\rm C}/J$. Figure 2(b) shows the incident angle $\theta_{0}$ dependence of the photocurrent helicity asymmetry, which increases with the incident angle for the angle range from 0 to 45$^{\circ}$, and the signs are all reversed when the incident angle is changed from positive to negative. The photocurrent helicity asymmetry is only observed at oblique incidence. When the incident angle $\theta_{0}$ is set to be zero, no spin-polarized current is created because there is no optically induced in-plane spin polarization in the plane of electron according to the optical selection rules in the semiconductor. The current induced by the circularly polarized light at oblique incidence can be expressed as[22] $$\begin{align} J_{\rm C} =\gamma_{xy} t_{p} t_{s} SE_{0}^{2}P_{\rm circ}\sin \theta_{0} \sin({\beta/n}),~~ \tag {2} \end{align} $$ where $\gamma_{xy}$ is the nonzero component of the second-rank pseudotensor and is proportional to the spin-orbit coupling constant, $t_{s}$ and $t_{p}$ are transmission coefficients for linear $s$ and $p$ polarizations given by Fresnel's formula, $n$ is the sample index of refraction, $S$ is the spot area of the incident, $E_{0}^{2}$ and $P_{\rm circ}$ are the intensity and helicity of the incident light, and $\theta$ and $\beta$ are the incident and azimuth angles of the light. For Fresnel's formula, Eq. (2) can be rewritten as[23] $$\begin{align} J_{\rm C} =\,&\gamma_{xy} E_{0}^{2}{\rm S}_{0} P_{\rm circ}[2\sin (2\theta_{0})\sin({\beta/n})]/[(\cos\theta\\ &+\sqrt {n^{2}-\sin^{2}{\theta_{0}}})(n^{2}\cos\theta +\sqrt {n^{2}-\sin^{2}\theta_{0}})].~~ \tag {3} \end{align} $$ The result in Fig. 2(b) can be fitted well with Eq. (3). Furthermore, we measured the photocurrent helicity asymmetry as a function of the azimuth angle $\beta$. Figure 2(c) shows the azimuth angle $\beta$ dependence of the photocurrent helicity asymmetry with the incident angle at 30$^{\circ}$. As indicated by Eq. (3), the circular photogalvanic current $J_{\rm C}$ recorded from the $Y$ contacts is proportional to $\sin\beta$ while the sample is rotated around the normal. It is obvious that the photocurrent helicity asymmetry reaches zero when the propagation direction of the radiation light is parallel to the $Y$-direction. We note that the sign of the photocurrent helicity asymmetry reverses with the variety of the azimuth angle $\beta$. This observation further supports the measured photocurrent results from the linear spin splitting in our InGaAs/AlGaAs 2DEG sample. Furthermore, when the propagation direction of incident light is perpendicular to the $Y$-direction, the photocurrent helicity asymmetry in the plane of 2DEG has a different amplitude. These results indicate that there exists an anisotropic in-plane spin splitting in 2DEG.
cpl-36-7-077201-fig3.png
Fig. 3. (a) Phase angle $\varphi$ dependence of photocurrent in In$_{0.15}$Ga$_{0.85}$As/Al$_{0.3}$Ga$_{0.7}$As MQWs under different in-plane electric fields $E_{x}$. The photocurrent is measured at room temperature with the azimuth and incident angles of 0$^{\circ}$ and 30$^{\circ}$. Note that the curves in (a) are intentionally shifted for clarity. (b) In-plane electric fields $E_{x}$ dependence of the photocurrent helicity asymmetry at different temperatures.
Figure 3(a) further shows the total currents corresponding to the 1hh-1e transition as a function of phase angle $\varphi$ under electric fields along the $X$-direction, and the azimuth and incident angles are fixed to be 0$^{\circ}$ and 30$^{\circ}$. The influence of the bias on the photocurrent helicity asymmetry at different temperatures is shown in Fig. 3(b). The photocurrent helicity asymmetry is measured at the wavelength corresponding to the quantum well absorption maximum for different temperatures. The photocurrent helicity asymmetry approximately increases with the decrement of lattice temperature at a fixed electric field (actually the changing trend is complex at lower temperatures). We measure an increment of photocurrent helicity asymmetry with positive biases while a decreased amplitude is observed with negative biases. According to Ref.  [24], the photocurrent helicity asymmetry can be expressed as $$\begin{align} \frac{J_{\rm C}}{J}=\frac{\tau_{\rm s}}{2\tau_{0}}({\alpha_{_{\rm BIA}} +\alpha_{_{\rm SIA}}}),~~ \tag {4} \end{align} $$ where $\tau_{0}$ is the recombination lifetime of photoinduced electrons, $\tau_{\rm s}$ is the spin relaxation time, and $\alpha_{_{\rm BIA}}$ is the bulk inversion asymmetry (BIA) term, due to the lack of inversion symmetry in bulk of the material in which the heterostructure is made. In asymmetrical heterostructures, there is an additional contribution to the spin-orbit term, which is absent in the bulk, and it is caused by structure inversion asymmetry (SIA). Here $\alpha_{_{\rm SIA}}$ is proportional to the electric field $E$ acting on an electron: $\alpha_{_{\rm SIA}}=\alpha_{0}eE_x$, with $e$ the elementary charge and $\alpha_{0}$ a second spin-orbit constant determined by both the bulk spin-orbit interaction parameters and the properties of interface. Dependence of electron spin relaxation time on the applied bias can be considered. It can be linked to $\alpha_{_{\rm SIA}}$ (Rashba effect) on the Dyakonov–Perel electron spin relaxation time in the quantum wells. The electron spin relaxation time varies if the amplitude of electric fields along the $X$-direction increases as observed in (001) quantum wells.[10,25]
cpl-36-7-077201-fig4.png
Fig. 4. In-plane electric fields $E_{y}$ dependence of the photocurrent helicity asymmetry at different temperatures. The points are the experimental data, and the solid lines are the fitting result using Eq. (5).
As shown in Fig. 4, when the electric fields are applied along the $Y$-direction, it is obvious that the photocurrent helicity asymmetry changes like parabolas with varied electric fields, especially at low temperatures. According to Eq. (4), at a specified temperature (such as 77 K), the lifetime $\tau_{0}$ of photoinduced electrons is a constant, $\alpha_{_{\rm SIA}}$ is slightly influenced by the electric fields along the $Y$-direction,[25] thus $\tau_{\rm s}$ is the only free parameter in Eq. (4). From Fig. 4, one can infer that the decrease of photocurrent helicity asymmetry with the increase of electric field is ascribed to the acceleration of spin relaxation with the increase of electric field. This acceleration of spin relaxation is supposed to be owed to an enhancement of hot phonon effect in drifting electrons,[26,27] while in this narrow quantum well, the electron spin relaxation time $\tau_{\rm s}$ varies approximately as $T_{\rm e}^{-1}\tau_{\rm p}^{-1}$, where $\tau_{\rm p}$ is the momentum relaxation time, $T_{\rm e}$ is the hot-electron temperature. In the temperature range of 77–297 K, the longitudinal optical phonon (LO phonon) scattering is supposed to be dominant. Equation (4) based on the D-P mechanism should be expressed as[24,26,28] $$\begin{alignat}{1} \frac{J_{\rm C}}{J}=\frac{({\alpha_{_{\rm BIA}} +\alpha_{_{\rm SIA}}})\varepsilon}{2\tau_{0} \tau_{\rm p} T_{\rm L}}\frac{1}{1+{m^{\ast}\hslash \omega_{0} \nu_{\rm d}^{2}}/{k_{\rm B}^{2} T_{\rm L}^{2}}},~~ \tag {5} \end{alignat} $$ where $\varepsilon$ is a material-specific parameter relating to the spin-orbit splitting, $T_{\rm L}$ is the lattice temperature, $\omega$ is the frequency of LO phonons, $m^\ast$ is the effective mass of the electron, $\nu_{\rm d}$ is the drift velocity of photoinduced electrons and assuming the drift velocity $\nu_{\rm d}$ is unsaturated, namely, $\nu_{\rm d}$ is proportional to the electric field $E$ acting on the $Y$-direction: $\nu_{\rm d}=\mu E_y$ with $\mu$ the photoinduced electron mobility which is supposed to be contributed mainly by the scattering of LO phonons especially at the measured temperatures. The experimental data shown in Fig. 4 are fitted by Eq. (5), which reveals the electric field and lattice temperature dependence of the photocurrent helicity asymmetry. Moreover, the hot phonon effect is proportional to the photoinduced electron mobility. At lower temperatures, with higher mobility of the photogenerated electrons, the hot phonon effect is stronger and the spin relaxation is enhanced. As a result, the photocurrent helicity asymmetry decreases quickly, while at room temperature, the photogenerated electrons hold smaller mobility. Hence, there is a weak hot phonon effect at the measured electric fields In conclusion, we have investigated the spin polarization in undoped InGaAs/AlGaAs multiple quantum wells. The results indicate that there exists an anisotropic in-plane spin splitting in 2DEG. We also investigate the effect of different-oriented in-plane electric fields on spin transport in an undoped In$_{0.15}$Ga$_{0.85}$As/Al$_{0.3}$Ga$_{0.7}$As MQWs. The photocurrent helicity asymmetry varies strongly with the different oriented in-plane electric fields, and these characteristics are interpreted on the basis of the Rashba spin-orbit terms and the hot phonon effect in the presence of the in-plane electric fields. Our findings will be beneficial for a further understanding of spin splitting phenomena as well as for spintronics applications using spin transport under electric fields in semiconductors. 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