Spin photocurrent spectra induced by Rashba and Dresselhaustype circular photogalvanic effect at interband excitation in InGaAs/GaAs/AlGaAs step quantum wells
 Jinling Yu^{1, 3}Email author,
 Shuying Cheng^{1},
 Yunfeng Lai^{1},
 Qiao Zheng^{1} and
 Yonghai Chen^{2}
DOI: 10.1186/1556276X9130
© Yu et al.; licensee Springer. 2014
Received: 3 February 2014
Accepted: 7 March 2014
Published: 19 March 2014
Abstract
Spin photocurrent spectra induced by Rashba and Dresselhaustype circular photogalvanic effect (CPGE) at interband excitation have been experimentally investigated in InGaAs/GaAs/AlGaAs step quantum wells (QWs) at room temperature. The Rashba and Dresselhausinduced CPGE spectra are quite similar with each other during the spectral region corresponding to the transition of the excitonic state 1H1E (the first valence subband of heavy hole to the first conduction subband of electrons). The ratio of Rashba and Dresselhausinduced CPGE current for the transition 1H1E is estimated to be 8.8±0.1, much larger than that obtained in symmetric QWs (4.95). Compared to symmetric QWs, the reduced well width enhances the Dresselhaustype spin splitting, but the Rashbatype spin splitting increases more rapidly in the step QWs. Since the degree of the segregation effect of indium atoms and the intensity of buildin field in the step QWs are comparable to those in symmetric QWs, as proved by reflectance difference and photoreflectance spectra, respectively, the larger Rashbatype spin splitting is mainly induced by the additional interface introduced by step structures.
Keywords
Circular photogalvanic effect spectroscopy Reflectance difference spectroscopy Rashba and Dresselhaus spin splitting Inplane optical anisotropyBackground
Recently, spintronics has attracted much attentions due to its significant role in both fundamental research and possible device applications [1–10]. The most critical issues for realizing spintronic devices are the generation and manipulation of spinpolarized carriers in lowdimensional systems [2, 11]. Spinorbit coupling (SOC) and the resulting spin splitting in a twodimensional system have been used to create and manipulate spinpolarized carriers in nonmagnetic materials without external magnetic field [1, 12–14]. There are two kinds of SOC according to different sources of inversion asymmetry: Dresselhaus SOC induced by the bulk inversion asymmetry (BIA), [15] and Rashba SOC induced by structure inversion asymmetry (SIA) [16]. These two terms can interfere with each other and result in an anisotropy of spin splitting. They can cancel each other when the Rashba and Dresselhaus terms have equal strength, which will lead to a zero spin splitting in certain k directions. [2] Therefore, it is important to control the value of these two components for spintronic device applications. The Rashba SOC can be tuned by external field [17], uniaxial strain [18, 19], and the asymmetric potential gradients in the quantum wells (QWs) [7, 8, 20], while the Dresselhaus SOC is determined by the materials and the size quantization of the electron wave vector k along the growth direction z, that is, $\u3008{k}_{z}^{2}\u3009$= (π/w)^{2} for an infinitely high potential well of width w[9]. Nowadays, there are lots of theoretical [21, 22] and experimental investigations [7, 20] concerning the influence of the asymmetric potential gradients on the spin splitting of the electrons. However, there is seldom report investigating the influence of the asymmetric gradients on the spin splitting when both the electron and holes are involved. Circular photogalvanic effect (CPGE) is an effective experimental tool to measure spin splitting in lowdimensional semiconductor system at room temperature [10], which is induced by unbalanced occupation of carriers in momentum space excited by circularly polarized light as a result of SOC and optical selection rules [4, 23]. Spin photocurrent spectra of CPGE excited by interband transition, which is firstly observed by Bel’kov et al. [24], are a powerful tool to investigate the spin splitting when both the electron and holes are involved, especially when excitonic effect is dominant [19]. Besides, CPGE current with interband resonance excitation shows much stronger intensity than that with innerband excitation [5]. Thus, some unmeasurable features in the innerband excitation may be detectable by this highly sensitive interband resonance excitation. Step QW structure will not only destroy the structure inversion symmetry by a step potential, but also introduce an additional interface compared to symmetrical QWs. Therefore, step QW structure is of fundamental interest in the study of asymmetric gradientinduced and interfaceinduced Rashba spin splitting [22].
In this paper, we use CPGE spectra at interband excitation to study the Rashba and Dresselhaus spin splitting in an undoped asymmetric In_{0.15}Ga_{0.85}As/GaAs/AlGaAs step QWs. For an undoped QWs with high crystal quality, the excitonic effect will play a dominant role in the photocurrent spectra. In this case, both of the electron and holes will contribute to the photocurrent [25]. We separate the CPGE spectra induced by Rashba and Dresselhaus spin splitting, respectively, and we find that the Rashba and Dresselhausinduced CPGE spectra are quite similar with each other during the spectral region corresponding to the transition of the excitonic state 1H1E (the first valence subband of heavy hole to the first conduction subband of electrons). The ratio of the CPGE current induced by Rashba and Dresselhaus spin splitting for the transition of 1H1E is much larger than that in the symmetric QWs reported in our previous work (i.e., 8.8 vs 4.95). Although the reduced well width enhances the Dresselhaustype spin splitting compared to the symmetric QWs, the Rashbatype spin splitting in the asymmetry step QWs increases more rapidly. By using reflectancedifference spectrum and photoreflectance spectrum, we find that the degree of the segregation effect of indium atom and the intensity of the buildin field in the step QWs are comparable to those in symmetric QWs. So, the larger Rashba SOC may be mainly induced by the one more interface present in the step structures.
Methods
The sample studied here is asymmetric In_{0.15}Ga_{0.85}As/GaAs/Al_{0.3}Ga_{0.7}As step QWs grown on (001) SIGaAs substrate by molecular beam epitaxy. After a 2,000Å buffer layer is grown, ten periods of 50 Å In_{0.15}Ga_{0.85}As/50 ÅGaAs/100 Å Al_{0.3}Ga_{0.7}As are grown. The grown temperature of In_{0.15}Ga_{0.85}As and Al_{0.3}Ga_{0.7}As are 540°C and 580°C, respectively. Then, 500Åthick Al_{0.3}Ga_{0.7}As layer and 100Å GaAs cap layer are deposited. All epilayers are intentionally undoped and the InGaAs layers are fully strained since their thickness is far below the critical thickness. The sample is cleaved along [110] and [1$\stackrel{\u0304}{1}$0] (denoted as the x^{′} and y^{′} directions, respectively) into a square of 5 mm × 5 mm with four pairs of ohmic contacts 4 mm apart along the x^{′}, y^{′} and diagonal directions, respectively, as shown in figure one(a) in [26]. The ohmic contacts are made by indium deposition and annealed at about 420°C in nitrogen atmosphere.
For optical interband excitation, a supercontinuum laser source combined with a monochromator is used providing radiation of wavelength in the range between 800 and 950 nm. The supercontinuum laser provides 5ps pulses with a repetition rate of 40 MHz and an average power of 4 W. Then, the monochromatic light with a linewidth of 1.5 nm goes through a polarizer and a photoelastic modulator (PEM) to yield a periodically oscillating polarization between right (σ^{}) and left (σ^{+})hand circularly polarized light. The light spot on the sample is rectangular of 2 × 3.8 mm with a power of about 150 µW at 950 nm (see figure one(a) in [26]). The photogalvanic current is measured in the unbiased structures at room temperature via a preamplifier and then is recorded by a lockin amplifier in phase with the PEM. Besides, in order to normalize the data thus enabling a better comparison between BIA and SIA, a common photocurrent j_{0} under direct current (dc) bias is also measured by a chopper and a lockin amplifier. Thus, we can use the common photocurrent j_{0} as the denominator for normalizing the CPGE current to eliminate the influences of the anisotropic carrier mobility and carrier density in different directions [26].
In order to get the knowledge of the symmetry of the QW system, we perform reflectancedifference spectrum (RDS) measurement. RDS is an interfacesensitive and nondestructive technique [27, 28], and it can precisely measure the inplane optical anisotropy (IPOA) between the [110] and $\left[1\stackrel{\u0304}{1}0\right]$ directions. Both of bulklike and interfacelike symmetry reduction effects can introduce IPOA into the (001)grown zinc blende QWs. The former one can be induced by electric field [29, 30], compositional variation across the QWs, uniaxial strain [31, 32], and the atomic segregation effect [28], while the latter one can be introduced by anisotropic interface structures [31] and anisotropic interface chemical bonds [33]. Therefore, from the RDS measurement, one can obtain the symmetry properties of QWs. The setup of our RDS is the same as that used in [27], from which we can obtain the relative reflectance difference between [110] and [1$\stackrel{\u0304}{1}$0] directions, i.e., $\mathrm{\Delta r}/r=2({r}_{\left[110\right]}{r}_{\left[1\stackrel{\u0304}{1}0\right]})/({r}_{\left[110\right]}+{r}_{\left[1\stackrel{\u0304}{1}0\right]})$. Besides, the reflectance spectrum Δ R/R can be obtained simultaneously during RDS measurements [27, 32]. Here, R is the reflectivity of the sample, and Δ R/R is the reflectivity difference of the sample with and without QW layers. To estimate the value of internal field in the sample, we perform PR measurement. The setup of the PR system is the same as that used in [26].
Results and discussion
which describes the dependence of the CPGE current on the angle of incidence θ obtained theoretically [2, 34]. Here, $A=4{E}_{0}^{2}\mathrm{\kappa \gamma}{P}_{\text{circ}}$, E_{0} is the electric field amplitude of the incident light, κ is the absorption coefficient, γ = α or β, P_{circ} is the degree of circular polarization, i.e., ${P}_{\text{circ}}=({I}_{{\sigma}^{+}}{I}_{{\sigma}^{}})/({I}_{{\sigma}^{+}}+{I}_{{\sigma}^{}})$, and n is the refractive index of the QWs material. It can be seen from Figure 3 that the experimental data agree well with the phenomenological theory of CPGE. In the fittings, n is adopted to be 3.55 according to [35], and the parameter A is fitted to be 1,232 ± 15 and 140 ± 10 for SIA and BIAinduced CPGE current, respectively. Thus, we can obtain α/β = 1,232 ± 15 / (140 ± 10) = 8.8 ± 0.1, much larger than the value obtained in symmetric InGaAs/AlGaAs QWs (4.95) investigated in our previous work [26]. This indicates that SIA is the dominant mechanism to induce spin splitting in the step InGaAs/GaAs/AlGaAs QWs. The normalized CPGE signal induced by BIA is estimated to be 0.26 ± 0.01 at an incident angle of 40 °, which is larger than that obtained in the symmetric InGaAs/AlGaAs QWs (0.22 ± 0.01) reported in our previous work [26]. This can be attributed to the size quantization effect of the electron wave vector k along the growth direction z, since the effective well width is reduced in the step QWs compared to the symmetric QWs, and the Dresselhaustype spin splitting increases with decreasing well width of QWs according to [9]. Although the Dresselhaus SOC is enhanced in step QWs, the Rashba SOC increases more rapidly, which results in larger RD ratio in the step QWs. In order to find out the reason for the strong Rashbatype spin splitting, we further perform PR and RDS measurements.
For interband excitation of undoped QWs investigated in our case, both electrons and holes may contribute to the CPGE current. Which one plays a dominant role is closely related to their spin relaxation time. The spin relaxation time of electrons in an undoped GaAs/AlGaAs QWs with a well width of 7.5 nm is measured to be 70 ps [37], while that of holes is reported to range from 4 ps [38] to as long as 1,000 ps [39] depending on the doping levels, temperature, and quantum well structures. A recent experiment investigation on ptype QWs concludes that the spin relaxation time of holes should be at least 100 ps and approaching the nanosecond (ns) range at a temperature of 4 K [40]. Besides, a more recent theoretical analysis found that the spin relaxation time can be of the same order of magnitude for electrons and holes for quantum dots with large lateral dimensions [41]. This qualitative conclusion should be of some relevance also for QWs [42]. Therefore, we suppose that the electrons and holes may contribute to the observed CPGE current at the same order.
Here, Γ is the linewidth of the transition, and E_{ n m }(P_{ n m }) is the energy (probability) of the transition between n E (the n th conduction subband of electrons) and m LH (the m th valence subband of light holes) or between n E and m HH. Thus, by fitting the theoretical calculated DP with that obtained by experiments, we can determine the structure parameters of the QWs, such as the interface potential parameters P_{ i } (i = 1, 2, 3), segregation length of atoms l_{ i } (i = 1, 2, 3), and anisotropy strain ε_{ x y }.
Using Equation 4, we can estimate the DP values of the transition for the excitonic states 1H1E and 1L1E to be 0.5 % ± 0.5% and 6.3 % ± 0.5%, respectively. In order to calculate the theoretical DP value of the transitions of the QWs, we should first estimate the interface potential P_{0} for an ideal InAsAl_{0.3}Ga_{0.7}As, GaAsInAs, and AlAsGaAs interfaces, respectively. Using the perturbed interface potential, the averaged hybrid energy difference of interface, and the lattice mismatch models, and then adding them up, we can obtain the value of P_{0} for an ideal InAsAl_{0.3}Ga_{0.7}As interface to be 639 meV Å [46]. The P_{0} at GaAsInAs and AlAsGaAs interfaces are reported to be 595 and 400 meV Å [27, 47], respectively. Since the InAsonAl_{0.3}Ga_{0.7}As interface tends to be an ideal and abrupt interface, we adopt P_{1} = P_{0}. Due to the segregation effect of indium atoms at the GaAsonInAs interface, P_{2} may not be equal to P_{0}. Therefore, we treat P_{2} as a fitting parameter. According to [27], the interface potential P_{3} for AlAsonGaAs interface is fitted to be 440 meV Å, due to the anisotropic interface structures. Thus, adopting P_{1} = 639 meV Å, P_{3} = 440 meV Å, and internal electric field F = 12.3 kV/cm (obtained by PR measurements) and treating the interface potential P_{2} and the segregation length l_{1} = l_{2} = l_{3} = l as fitting parameters, we fit the theoretical calculated DP value to that of experiments. When we adopt P_{2} = 650 meV Å, l = 2.8 nm, the DP values of the transition 1H1E and 1L1E can be well fitted, and the main features of the RD spectrum are all well simulated (see Figure 5, Δ M∝Δ r/r). The large segregation effect of indium atoms and the strong internal field reduce the step well into an irregular well, as shown in the inset of Figure 5. This will result in large Rashba spin splitting according to [8, 26]. However, we find that the intensity of the internal field and the segregation length of the indium atoms for the step QWs are comparable to those in symmetric QWs, which indicate that the Rashba SOC induced by these two factors are at the same scale and they are not the main reasons for the larger Rashba spin splitting in the step QWs. On the other hand, the interface in QWs will also introduce Rashbatype spin splitting, which is related to some band discontinuities in valence bands at heterointerfaces [22, 48]. Since the step QW structures will introduce one additional interface compared to symmetric QWs and this additional interface will introduce additional Rashba spin splitting, the larger Rashba spin splitting in the step QWs may be mainly induced by this interface Rashba effect. It is worth mentioning that the interface or the segregation effect alone will not necessarily lead to larger Rashba spin splitting, and only when they are combined with large electric field or the presence of a Hartree potential gradient in the asymmetric system will finally result in a significant spin splitting [48].
Conclusions
In conclusion, we have experimentally investigated the spin photocurrent spectra induced by Rashba and Dresselhaustype CPGE at interband excitation in InGaAs/GaAs/AlGaAs step QWs at room temperature. It is found that the line shape of CPGE spectrum induced by Rashba SOC is quite similar to that induced by Dresselhaus SOC during the spectral region corresponding to the transition of the excitonic state 1H1E. The ratio of Rashba and Dresselhausinduced CPGE current for the transition of the excitonic state 1H1E is estimated to be 8.8 ± 0.1, much larger than that reported in the symmetric QWs in our previous work (i.e., 4.95 in [26]). We also find that, compared to symmetric QWs, the reduced well width in the step QWs enhances the Dresselhaustype spin splitting, while the Rashbatype spin splitting increases more rapidly. Since the intensity of the buildin field and the degree of the segregation effect in the step QWs are comparable to those in symmetric QWs, which are evident from RDS and PR measurements, the larger Rashba spin splitting in the step QWs are mainly induced by the additional interface introduced by step structures.
Abbreviations
 BIA:

bulk inversion asymmetry
 CPGE:

circular photogalvanic effect
 DP:

degree of polarization
 IPOA:

inplane optical anisotropy
 PEM:

photoelastic modulator
 PR:

photoreflectance
 QWs:

quantum wells
 RDS:

reflectancedifference spectrum
 SIA:

structure inversion asymmetry
 SOC:

spinorbit coupling
 1H1E:

the first valence subband of heavy hole to the first conduction subband of electrons.
Declarations
Acknowledgements
The work was supported by the National Natural Science Foundation of China (No. 60990313, No. 61006003, No. 61306120), the 973 program (2012CB921304, 2013CB632805), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (Grant No. LXKQ201104), the fund of Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences (2008DP173016), and the Foundation of Fuzhou University of China (Grant No. 022498).
Authors’ Affiliations
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