APPLIED PHYSICS LETTERS 93, 262104 共2008兲

Influence of the illumination on weak antilocalization in an AlxGa1−xN / GaN heterostructure with strong spin-orbit coupling W. Z. Zhou,1,2,3,a兲 T. Lin,3 L. Y. Shang,3 L. Sun,3 K. H. Gao,3 Y. M. Zhou,3 G. Yu,3 N. Tang,4 K. Han,4 B. Shen,4 S. L. Guo,3 Y. S. Gui,3 and J. H. Chu1,3,a兲 1

Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200062, People’s Republic of China 2 Physical Science and Technology College, Guangxi University, Nanning, Guangxi 530004, People’s Republic of China 3 National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, People’s Republic of China 4 State Key Laboratory of Artificial Microstructure and Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, People’s Republic of China

共Received 24 September 2008; accepted 25 November 2008; published online 30 December 2008兲 The weak antilocalization effects of the two-dimensional electron gas in a high mobility AlxGa1−xN / GaN heterostructure have been investigated by means of magnetotransport measurements before and after illumination. The zero-field spin splitting mainly arising from the Rashba spin-orbit coupling effect as a function of electron concentration as well as a function of temperature is studied using the weak antilocalization analysis. The Rashba spin-orbit coupling constant ␣ deduced using the weak antilocalization analysis shows a rapid decrease with the increase of the measured electron concentration. © 2008 American Institute of Physics. 关DOI: 10.1063/1.3049615兴 Two-dimensional electron gases 共2DEGs兲 in AlxGa1−xN / GaN heterostructure are very promising candidates for future spintronic applications based on the facts that1,2 GaN-based diluted magnetic semiconductors are prospective materials for spin injection or spin analyzer because they show Curie temperatures above room temperature and are expected to be a good match to AlxGa1−xN / GaN heterostructures. Besides, 2DEGs in AlxGa1−xN / GaN heterostructures are potential candidates for gate-controlled spin precession utilizing the Rashba effect3 induced by structural inversion asymmetry 共SIA兲 of quantum well. In wurtzite AlxGa1−xN / GaN heterostructures, the zerofield spin splitting can originate from the Rashba effect and the effect induced by the lack of inversion symmetry of the wurtzite-type lattice, i.e., the bulk inversion asymmetry 共BIA兲. The electric field originating from the BIA in wurtzite AlxGa1−xN / GaN heterostructures is oriented along the 共0001兲 direction and thus parallel to the macroscopic electric field in the SIA quantum well.1,2 And both the Rashba and BIA terms are linear scaling of the Fermi wave vector k f .4 The Rashba spin-orbit 共SO兲 coupling is of particular interest due to its potential applications in spin-field-effect transistor in the ballistic regime, as it can be controlled by an applied gate voltage.5 The zero-field spin splitting in AlxGa1−xN / GaN heterostructures has attracted considerable and continuously growing interest for the application in the spintronic devices. Recent experiments based on Shubnikov–de Haas 共SdH兲, weak antilocalization 共WAL兲, and circular photogalvanic measurements have given conflicting results such as the original mechanisms for the zero-field spin splitting of the 2DEG, as well as the magnitude of SO interaction in wurtzite AlxGa1−xN / GaN heterostructures.1,2,4,6–11 Thillosen et al. a兲

Authors to whom correspondence should be addressed. Electronic addresses: [email protected] and [email protected].

0003-6951/2008/93共26兲/262104/3/$23.00

found that the SO coupling constant ␣ obtained from the WAL analysis is identical though the AlxGa1−xN barrier layers as well as the electron concentration are different.2 The deduced SO coupling constant ␣ from the WAL analysis independent of the AlxGa1−xN barrier layers as well as the electron concentration was also presented by Kurdak et al.4 and Schmult et al.10 Thillosen et al. concluded that the SO coupling present in AlxGa1−xN / GaN heterostructures seems to be completely determined by the BIA of the GaN lattice and cannot be controlled by a gate.2 In a recent study, it was suggested that the zero-field spin splitting mainly arises from the Rashba effect in wurtzite AlxGa1−xN / GaN heterostructures in virtue of the investigation of the shift of the beating nodes and the change of WAL by the illumination.12,13 To help resolve these issues, we have performed WAL measurements under different illumination time on AlxGa1−xN / GaN heterostructure in this letter. The deduced Rashba SO coupling constant ␣ using the WAL analysis showed a rapid decrease with the measured electron concentration. Al0.22Ga0.78N / GaN heterostructure was grown by means of metal organic chemical vapor deposition 共MOCVD兲 on the 共0001兲 surface of sapphire substrate. The layer sequence is depicted in the inset of Fig. 1共a兲. Previously, the MOCVD growth process has been discussed for a similar sample in detail.13 SdH and WAL measurements were performed in low temperatures and magnetic fields were applied perpendicularly to the heterointerface. A light-emitting diode with the wavelength of 390 nm was used to illuminate the sample at the temperature of 1.4 K. The 2DEG concentration is gradually increased after each illumination. Due to the persistent photoconductivity effect, the increased 2DEG concentration persists for a long time, which is much longer than the time of the WAL measurements. Figure 1共a兲 shows the diagonal magnetoresistance ␳xx and the transverse magnetoresistance ␳xy of the 2DEG in the Al0.22Ga0.78N / GaN heterostructure as a function of the ap-

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FIG. 1. 共Color online兲 共a兲 The oscillatory magnetoresistance ␳xx and the transverse magnetoresistance ␳xy of the 2DEG as a function of the applied magnetic field B perpendicular to the heterointerface at 1.5 K. The inset shows a schematic illustration of the layer sequence of the sample. 共b兲 The magnetoresistance ␳xx共B兲 − ␳xx 共0兲 as a function of the magnetic field B in the low magnetic field range at different temperatures. The vertical dash line at B = 0 mT is merely a guide for the eye.

FIG. 2. 共Color online兲 共a兲 Quantum conductivity correction curves ⌬␴ = ␴共B兲 − ␴共0兲 in units of 2␲e2 / h as a function of the transport field Btr at different temperatures 共solid symbols兲. Solid lines represent the fit by a model in Ref. 14. 共b兲 Temperature dependence of the inelastic scattering rate 1 / ␶␾ extracted from the fits of the WAL cures 共solid symbols兲. The solid line shows the linear dependence of 1 / ␶␾ on temperature at T 艋 8 K.

plied magnetic field perpendicular to the heterointerface at 1.5 K. The electron concentration n = 8.87⫻ 1012 cm−2 and mobility ␮ = 0.81⫻ 104 cm2 / V s of the 2DEG are extracted from the SdH measurements at 1.5 K. The electron effective mass of the 2DEG in the Al0.22Ga0.78N / GaN heterostructure is 0.23m0 共where m0 is the free electron mass兲 obtained from the temperature dependence of the SdH oscillations. According to Btr = ប / 2eltr2 共where Btr is the transport field, ប is the Planck constant over 2␲, ltr = vF␶tr is the mean free path, and 14 vF is the velocity of electron at Fermi surface兲, the transport field Btr is estimated to be 2.08 mT, below which electrons move diffusively.14,15 And the transport scattering time ␶tr and the mean free path ltr are estimated to be 1.06 ps and 397 nm, respectively. Figure 1共b兲 presents the measured low-field magnetoresistance as a function of the applied magnetic field for the sample at different temperatures. A clear WAL peak was observed in the vicinity of B = 0 for all temperatures. The WAL peak decreases with the increase of the temperature. In order to extract estimates of the spin splitting from the WAL effect, the experimental curves were fitted by the theoretical model developed by Golub14 which is valid in a wide range of magnetic field and parameters ⍀␶tr, where ⍀ is the SO frequency. It should be noted that only Rashba effect or the linear BIA term is considered in this model quantifying both contributions. The curves of experimental conductivity correction of the 2DEG in the sample as a function of the transport field Btr in the range of very low magnetic field at different temperatures are shown in Fig. 2共a兲. A good fit to the experimental curves has been achieved at different temperatures 关see Fig. 2共a兲兴. The corresponding values of ⍀␶tr are obtained to be 0.89 and is almost a constant value in the measured temperature range. The extracted value of ␶tr / ␶␸ by fitting the experimental conductivity corrections increases with the increase of temperature. Since the Rashba term and the linear BIA term cannot be distinguished here, an effective SO coupling still labeled as Rashba term ⌬R comprising both contributions is considered. Accordingly the zero-field spin splitting energy is defined to be ⌬R = 2ប⍀.16–18 The zero-field

spin splitting energy is estimated to be 1.11 meV, which give the effective Rashba SO coupling constant ␣ expressed as ␣ = ⌬R / 2k f to be 7.42⫻ 10−11 eV cm. According to the expression lso = ប2 / 冑2␣m*, the spin precession length lso is achieved to be 315 nm using the known values of ␣ extracted from the WAL analysis. In the measured temperature range, the inelastic scattering rate scales as 1 / ␶␾ ⬀ T at T 艋 8 K 关see Fig. 2共b兲兴. At low temperatures, theories based on electron-electron interaction predict the inelastic scattering rate to scale linearly with temperature at T ⬍ ប / kB␶tr and quadratically with temperature at T ⬎ ប / kB␶tr 共Ref. 19 and references therein兲. For the sample, the characteristic temperature Tc = ប / kB␶tr is determined to be about 7.2 K based on the known value of ␶tr. Experimental values for ␶␾ coincide well with the theoretical prediction in the temperature range of T 艋 8 K. At T 艌 8 K, the coincidence between the experimental result and the theoretical prediction is not verified since the number of data points at higher temperature is not enough. The low-field quantum conductivity correction data for the sample at different electron concentrations at 1.4 K is shown in Fig. 3, where the solid lines represent the fit still by the model in Ref. 14. The magnetic field Bmin shifts to lower value of B / Btr when the electron concentration increases 共see Fig. 3兲, where Bmin is the magnetic field at which the conductivity correction minimum occurs in Fig. 3 or 2共a兲 关or the magnetic field at which the magnetoresistance maximum occurs in Fig. 1共b兲兴. The extracted value of ⍀␶tr by fitting the experimental curves decreases when the electron concentration increases. The calculated zero-field spin-splitting energy ⌬R = 2ប⍀ decreases with the increase of the electron concentration due to the decrease of ⍀␶tr with the increase of the measured electron concentration. The extracted SO coupling constant ␣ and the SO scattering time ␶so = 共2⍀2␶tr兲−1 are plotted as a function of electron concentration n in Fig. 4. The guide lines in Fig. 4 tell that the illumination makes the SO interaction weak and thus makes the SO scattering time enhanced though the error bars of the dependence of the Rashba SO coupling constant ␣ and the SO scattering time ␶so on the electron concentration are relative large.

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of the origin of the carriers and the change of the carriers under illumination. And the quantitative expression between the Rashba SO coupling constant and the 2DEG concentration in AlGaN / GaN heterostructures is needed to investigate in a future study. Also, these observations in the study may evoke further experimental and theoretical investigations to clarify the relation between Rashba SO coupling constant and the 2DEG parameters quantitatively in AlGaN / GaN heterostructures. Those works will be carried out in a future study.

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n=9.04X10 cm 12 -2 n=9.03X10 cm 12 -2 n=9.01X10 cm 12 -2 n=8.99X10 cm 12 -2 n=8.91X10 cm 12 -2 n=8.87X10 cm

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Appl. Phys. Lett. 93, 262104 共2008兲

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FIG. 3. 共Color online兲 Quantum conductivity correction curves ⌬␴ = ␴共B兲 − ␴共0兲 in units of 2␲e2 / h as a function of the transport field Btr at different electron concentrations at the temperature of 1.4 K 共solid symbols兲. The curves are vertically shifted for clarity. Solid lines represent the fit by a model in Ref. 14.

If the zero-field spin splitting originates from the BIA contribution, the increased k f should increase the spin splitting energy, which is contrary to the results. Therefore, the zero-field spin splitting mainly arises from the Rashba effect.12,13 It should be noted that in Fig. 3 the magnetic field Bmin will shift to higher value of B / Btr when the electron concentration increases if the zero-field spin splitting originates from the BIA contribution,20 which also gives the evidence of the zero-field spin splitting mainly arising from the Rashba effect. According to the theoretical expression ␣ = ប2eE / 4m*Eg 共where E is the electric field at the heterointerface of AlxGa1−xN / GaN heterostructure, and Eg is the width of the gap of quantum well兲,21 the electric field at the heterointerface is also weakened after each illumination. In order to extract the expectation value of the electric field variation along with the increase of electron concentration, a detailed calculation of the electron concentration and conduction and valence band edges of AlGaN / GaN heterojunction based on a self-consistent solution of the Schrödinger and Poisson equations,22 including the charge balance equation and the effect of exchange correlation on the Coulomb interaction23 should be performed based on the assumptions

FIG. 4. 共Color online兲 Dependence of the Rashba SO coupling constant ␣ 共solid symbols兲 and the SO scattering time ␶so 共open symbols兲 extracted from the fits of the WAL cures on the electron concentration of the Al0.22Ga0.78N / GaN 2DEG. The lines are merely guides for the eye.

This work was supported by the special funds for major state basic research project 共Grant No. 2007CB924900兲, the National Natural Science Foundation of China 共Grant No. 60221502兲, the National Science Foundation for Postdoctoral Scientists of China 共Grant No. 20070420634兲, the Scientific Research Foundation of GuangXi University 共Grant No. X071109兲, and the Scientific Research project of Science and Technology Commission of Shanghai 共Grant No. 07JC14059兲. 1

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