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Abstract
The anomalous circular photogalvanic effect (ACPGE) is observed in p-GaAs with a thickness of 2 μm at room temperature, in which circularly polarized light is used to inject spin-polarized carriers and the spin diffusion can generate a macroscopic detectable charge current due to the inverse spin Hall effect. The normalized ACPGE signals show first increasing and then decreasing with increasing the doping concentration. The role of the doping impurities is discussed by both extrinsic and intrinsic models, and both can well explain the variation of ACPGE with the doping concentration.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Spin Hall effect (SHE) [1] and inverse spin Hall effect (ISHE) [2,3] can realize the mutual transformation of spin current and charge current without magnetic material and applied magnetic field, which is of great significance for the research and development of spintronics devices. Both SHE and ISHE are based on intrinsic or extrinsic spin-orbit interactions (SOI). The intrinsic SOI comes from the breaking of time or space inversion symmetry and will bring about the spin splitting of the energy band. Common spin splitting includes Dresselhaus-type and Rashba-type introduced by bulk inversion asymmetry and structural inversion asymmetry, respectively. The extrinsic SOI is derived from impurity-induced spin deflection and scattering [4,5]. Among it, Mott skew scattering is a classical scattering model, in which spin-down and spin-up electrons can be scattered asymmetrically by charge centers.
SHE was first observed in bulk n-GaAs by Kato et al. [6], whereas the source of SOI is still controversial [6–11]. Kato et al. suggested that the observed effect is likely extrinsic due to the weak dependence on crystal orientation for the strained samples. Sih et al. [12] observed current-induced spin polarization of two-dimensional electron gas confined in AlGaAs quantum well. The quantum well was designed to be structural inversion symmetry to make the Rashba spin splitting small, thus it is inferred that the observed SHE is dominated by the scattering mechanism. Subsequently, the theoretical calculation of Tse et al. [10] supported the above two experiments. However, some researchers believe that SOI caused by impurity scattering is too weak to bring experimental results [7,8,13,14]. Wunderlich et al. [7] reported SHE of two-dimensional hole gas, and they explained it with intrinsic SOI since the impurity scattering should be negligible under this ‘pure’ system. Bernevig and S.C. Zhang suggested that the cubic Dresselhaus term in GaAs may produce a non-negligible intrinsic SOI [15], and they also proposed that the vertex correction due to impurity scattering is distinguishing for two-dimensional electron gas and two-dimensional hole gas [8], which resulted in different conclusions in Ref. [7] and Ref. [12]. All in all, most researchers determine the dominant mechanism via theoretical computation or rule out either intrinsic SOI or extrinsic SOI by the existence of intentionally doping or strain or electric field. To make clear the role of impurity scattering, a more direct investigation based on a series of doped samples is necessary, which is just the aim of this paper.
Because of the short spin diffusion length, a small sample structure and cryogenic temperature are often required for the detection of spin accumulation. According to our previous works [16–19], the circular photogalvanic effect (CPGE) is proved to be an effective and simple means of studying the intrinsic SOI [20]. Different from the CPGE of oblique incidence in high symmetric structures such as (001) GaAs, when circularly polarized light is incident vertically along (001) crystallographic axis, a charge current based on ISHE can be detected, which is called the anomalous circular photogalvanic effect (ACPGE). ACPGE has been observed in GaAs/AlGaAs two-dimensional electron gas, AlxGa1-xN/GaN two-dimensional electron gas, and InGaAs/AlGaAs non-doped multiple quantum well [21–23]. However, there is no further discussion on the source of SOI, and there has never been a study with doping concentration. In fact, no one has investigated ACPGE in bulk materials. In this work, we observed ACPGE in p-GaAs epilayer and conducted further doping-level variation experiments. The normalized ACPGE signals first increase and then decrease with the increase of impurity concentration, and two models dominated by extrinsic and intrinsic mechanisms respectively are discussed.
2. Sample structure and experimental method
A 2 μm thick Be-doped GaAs layer is grown by molecular beam epitaxy (MBE) on an undoped GaAs buffer layer (300 nm) at a growth temperature of 600 °C, with the semi-insulating (001) GaAs as substrate. The doping concentration NA is measured by the van der Pauw-Hall effect experiment at room temperature and is 9.8×1015, 3.2×1016, 3.1×1017, 6.3×1017, 3.4×1018, and 6.3×1018 cm-3, respectively. Besides, an undoped epitaxy wafer is grown for comparison. The samples are cleaved along [110] and [110] into 5 mm × 12 mm rectangles. As shown in Fig. 1, each sample has a pair of circular electrodes (diameter 0.25 mm), deposited by indium, and annealed at 420 °C for 12 minutes in a nitrogen atmosphere. Before the experiment, we performed current-voltage tests, and linear relationships indicate a good ohmic contact between samples and electrodes. A coordinate system can be established with the connection line of two circular electrodes as the y-axis and the vertical bisector of the two circular electrodes as the x-axis.
Fig. 1. Schematic diagram of the experimental principle. The dashed blue arrow represents the direction of the spin current, the black arrow indicates the direction of the spin polarization vector, and the red arrow indicates the direction of the transverse force on electrons.
The experiment setup is the same as that shown in Fig. 1(a) of Ref. [23]. Excitation light is provided by a mode-locked Ti-sapphire laser. The incident light passes through a polarizer and a photo-elastic modulator (PEM), of which the peak retardation is set to be λ/4, to be converted into a circularly polarized light with a periodic modulation of 50 kHz. An optical chopper with a rotation frequency of 230 Hz is also used to extract ordinary photocurrent signals. The Gaussian profile light beam irradiates vertically on the sample, with a diameter of 2 mm and an optical power of 80 mW. The sample is moved by the stepper motor with a step of 0.1 mm, so the light spot moves along the x-direction. The electrical signals are input to two lock-in amplifiers after passing through the preamplifier and are finally collected by the computer. To extract the inverse spin Hall effect charge current (JISHE) and ordinary photocurrent signal (JPC), the reference frequencies of the two lock-in amplifiers are set to 50 kHz and 230 Hz, respectively.
The schematic diagram of the experimental principle is shown in Fig. 1. Since the intensity of the light spot is a Gaussian distribution, the density of photogenerated spin-polarized carriers is also a Gaussian distribution. The density gradient of spin-polarized carriers leads to radial diffusion, thereby forming a spin current in the radial direction of the light spot. Based on the ISHE, the spin-polarized carriers are subjected to a transverse force that perpendicular to the directions of both spin current and spin polarization vector, resulting in a vortex current around the center of the light spot. As shown in Fig. 1, when the light spot is located on the left(right) side, the vortex current will have a net component in the + y(-y)-direction. In particular, when the light spot is located on the connection line between the two circular electrodes, the JISHE is zero because the vortex current has no net component on the y-axis.
3. Results and discussion
To determine the excitation wavelength used in this experiment, we obtained the ordinary photocurrent (JPC) spectrum of samples. The incident light spot is located at the coordinate origin, and circular electrodes are applied with 1V to measure the JPC. As shown in Fig. 2, the JPC almost disappears for wavelengths shorter than ∼870nm, which corresponds to the GaAs band edge (1.43 eV), reaches a maximum value at a photon energy of 1.363 eV (910 nm) and decreases slowly with further decrease of the photon energy. For photons with energy lower than the band edge, slant optical transition can occur due to the built-in surface electric field (see the inset of Fig. 2). We believe the quenching of the JPC of short wavelengths is due to the surface recombination effect. On the one hand, photons with shorter wavelengths are absorbed closer to the surface, where the photogenerated carriers can easily recombine via the surface states [24,25]. In this sense, photogenerated carriers excited by long-wavelength photons are less affected by surface states. On the other hand, due to a larger absorption coefficient for shorter-wavelength photons, the photogenerated carriers will concentrate on the surface, and the probability of direct recombination between photogenerated electrons and holes is also higher [26], resulting in a shorter lifetime of the photogenerated carriers and hence lower photoconductivity. In slant optical transition, the photogenerated electrons and holes are separated spatially, so the direct recombination of photogenerated electrons and holes will be suppressed. Of course, the optical transition probability will quickly decrease with the further decrease of the photon energy, give rise to the decreasing of the JPC with the increase of the wavelength.
Fig. 2. The JPC spectrum (NA=3.1×1017 cm-3). Inset: Energy band diagram of surface space charge region. The black solid circles represent photogenerated electrons, and the black hollow circles represent photogenerated holes. The optical transition is a slant in space.
Under an excitation wavelength of 910 nm, we obtain a mapping of JISHE in the plane of the sample (see Fig. 3(a)). When the light spot is scanned along the x-direction, a reversed sign of the charge current can be observed. The JISHE varies with position in the form of a sine function, which also confirms the rationality of the vortex current.
Fig. 3. (a) Mapping of JISHE in the plane. (b) JISHE normalized by JPC as the light spot moves along the x-axis.
To determine whether ACPGE occurs on the surface or in the bulk of p-GaAs, the layer-by-layer etching experiment of the sample was carried out. The H3PO4:H2O2:H2O solution with a volume ratio of 1:1:10 was used for etching at a rate of 500 nm/min. As shown in Fig. 4, when the etching depth is less than 2 μm (the thickness of the p-GaAs layer), JPC and JISHE are almost constant, and when the etching depth is over 2 μm, the signals sharply decrease and then keep weak. In other words, as long as the p-GaAs surface layer exists, the signals remain unchanged, which indicates that both of them come mainly from the surface space charge region of p-GaAs.
With light spot scanning along the x-axis (the dashed black arrow in Fig. 3(a)), the JISHE can reach its maximum amplitude, and we take the average absolute values of JISHE at ± 0.5 mm (red squares in Fig. 5(a)). For the same spot size and electrode spacing, the maximum amplitude of JISHE primarily depends on the strength of SOI, the spin polarizability, the diffusion coefficient (mobility), and the density of photogenerated carriers. The first two are related to ISHE, and the latter two can be reflected by the JPC (black solid circles in Fig. 5(a)). Taking into account the mobility [27] and spin relaxation time of electron and hole [28,29], we determined the non-equilibrium electron as the main contribution of JPC and JISHE. The JPC can be expressed as
where g is the generation rate of photogenerated electrons, ${\tau _0}$ is the lifetime of photogenerated electrons, and e is the elementary charge. $\mu$, E, S is the electron mobility, the electric field applied on the strip electrodes, and the cross-sectional area of current, respectively.Fig. 5. (a) JPC (black solid circles) and JISHE (red squares). (b) Experimental results and theoretical fitting of JISHE/ JPC for different doping concentrations.
Further, to extract parameters only associated with ISHE, we normalize JISHE with JPC (see Fig. 3(b)), and the average absolute values of JISHE/JPC at ± 0.5 mm (hereafter referred to JISHE/JPC, red squares in Fig. 5(b)) can be succinctly expressed as
where a is a constant independent of the doping concentration, $\gamma$ is a dimensionless parameter reflecting the strength of SOI, and $\eta$ is the spin polarizability. Below we will show that both parameters can be affected by the carrier density (or impurity density). Note that the same spatial source is the prerequisite for using JPC to normalize JISHE.Phenomenologically, the spin-charge drift-diffusion equations can be described as [4]
With doping concentration varying, the JISHE/JPC (red squares in Fig. 5(b)) changes by 20 times. Previously, we experimented with undoped epitaxial GaAs, and no ACPGE was observed at any wavelength (represented by a tiny value in Figs. 5(a) and 5(b)). ACPGE observed in doped samples proves that impurity scatting introduces significant extrinsic SOI. While the JISHE/JPC does not increase monotonically with the doping concentration because the surface electric field can reduce the spin relaxation time. Mature studies have shown that the surface electric field of p-GaAs is linearly proportional to the square root of the doping concentration [34,35]. Experimental results of K. C. Hall et al. [36–38] indicate that the spin relaxation time of electrons decays almost exponentially with the gate electric field since an additional Rashba component will generate a pseudo magnetic field in the plane [39], making the spin polarization vector away from the growth axis (z-direction). With doping concentration varying from 1×1016 cm-3 to 1×1019 cm-3, the ${\tau _s}$ of the electron in p-GaAs is ∼6×10−11 s at 300 K [40,41]. The ${\tau _s}$ was obtained by the optical-pumping method, whereas our experiment is an electrical measurement. According to the work of Jiti Nukeaw et al. [34], the surface electric field can increase from 45 kV/cm to about 400 kV/cm for the range of doping concentration in this experiment. Therefore, the influence of the surface electric field needs to be considered, and the relationship between spin relaxation time and doping concentration can be properly expressed as
Substitute Eq. (5), Eq. (6), and Eq. (7) into Eq. (2), there will be
Now we come to discuss the possibility of an intrinsic model. In doped bulk materials, extrinsic mechanisms are often used to explain the source of SOI [6,42], while intrinsic mechanisms are rarely considered a dominant factor. F. H. Mei et al. [43] reported ACPGE of the surface electron accumulation layer in InN films, and they believe a strong built-in electric field will enhance Rashba-type spin splitting, which leads to the observed ACPGE. Since ACPGE occurs in the surface space charge region of p-GaAs, the Rashba SOI caused by the built-in electric field may also be the dominant positive effect, i.e., ISHE is governed by the spin splitting of the conduction and/or valence bands in the plane perpendicular to the surface electric field. The coefficient $\gamma$ is proportional to the surface electric field, which is given by $\sqrt {{N_A}}$. In this case, the spin polarization is actually in the plane. When the system is excited vertically by a circularly polarized light, the photogenerated carriers with different in-plane wavevectors and hence different in-plane spin may generate a net polarization component in the z-direction, and then generate charge current under the ISHE. Unfortunately, there are few theoretical and experimental studies on how such spin polarization relaxes in the plane. In comparison to the above extrinsic model, here we only present a very simple model, which assumes that the spin polarization in the plane can be scattered by the impurity and spin relaxation time is inversely proportional to the impurity concentration. Supposing that the lifetime of the excited spin with no impurity scattering is $\tau _s^0$, then the impurity scattering induced one can be given by $\tau _s^i = C/{N_A}$. Now the total lifetime ${\tau _s}$ is simply determined by
With this simple model, we get ${J_{ISHE}}/{J_{PC}} \propto \sqrt {{N_A}}$ for small ${N_A}$, and ${J_{ISHE}}/{J_{PC}} \propto {1 / {{N_A}}}$ for large enough ${N_A}$ (see blue dot line in Fig. 5(b)). In general, this model can also well describe the variation of the experimental data shown in Fig. 5(b).
If the observed ACPGE has an intrinsic mechanism, it shall vary with the surface electric field, which can be changed by illumination. On the one hand, we carried out a power dependence experiment (take the sample with NA=3.1×1017 cm-3 as the representative). When the optical power varies from 40 mW to 160 mW, both JISHE and JPC increase linearly with increasing optical power (see Fig. 6). It should be noted that JISHE and JPC here are consistent with the definition in Fig. 5(a). In the formal experiment of this paper, we use an appropriate optical power of 80mW. On the other hand, we try to modulate the surface electric field with light above the band edge. Set the optical power of 910nm to 80mW, and the optical power of 532nm wavelength is set to 30μW, 130μW, 700μW, 5mW, and 50mW, respectively, which all do not change the JISHE and JPC. In conclusion, under the incident light of 910nm, it is difficult to change the surface electric field by varying the optical power. The modulated light with a wavelength of 532nm also did not generate carriers with a high enough density to change the surface electric field, which is consistent with the result shown in Fig. 2. For the intrinsic mechanism, more research is needed, such as applying strain to the sample without changing the doping level. There is a possibility that both mechanisms coexist in the observed ACPGE, no one seems to have discussed how electric field and impurity density affect $\gamma$ and ${\tau _s}$ in this complicated situation. We guess that it is probably a complex synthesis of the above two models.
4. Conclusion
In summary, we observed ACPGE in the surface space charge region of p-GaAs and take the doping concentration as the only controlled parameter. In the extrinsic model, the extrinsic SOI owing to the impurity scattering plays a dominant positive role. On the other side, the doping also increases the surface electric field and attenuates the spin relaxation time. In the intrinsic model, the surface electric field introduces the Rashba-type SOI, but the impurity may decrease the spin lifetime. Further, it is feasible to adjust the doping concentration and apply a controllable gate voltage for the design of spintronic devices.
Funding
National Natural Science Foundation of China (61627822, 61704121, 61991430); National Key Research and Development Program of China (2016YFB0400101, 2016YFB0402303, 2018YFA0209103, 2018YFE0204001); Natural Science Foundation of Tianjin City (19JCQNJC00700).
Disclosures
The authors declare no conflicts of interest.
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