Spin-dependent properties of two-dimensional AlGaN/GaN electron systems

摘要 我們研究了二維氮化鎵電子系統在旋光以及磁場下的電特性測量◦本論文包含下列幾部分 ◦ 一開始藉由波長325 nm的雷射激發，圓偏振所引導出來的自旋光電流在氮化鋁鎵/氮化鎵超晶格結構(Al0.15Ga0.85N/GaN superlattices)中第一次被觀察到 ◦ 藉由改變旋光的相位(例如:左旋光到右旋光)，可以改變光電流的方向◦ 其中，325nm引導出來的光電流大小比遠紅外光所引導出來的光電流多兩個數量級◦ 我們的結果證明了spin splitting 確實存在AlGaN/GaN superlattices的樣品中◦ 然而，為了探測造成 spin splitting的物理機制，我們測量了低溫下的二維電子在氮化鋁鎵/氮化鎵異質結構中的磁性傳輸◦藉由在Shubnikov–de Haas震盪的拍頻效應，我們可以量測零場的能階分裂◦ 我們的量測結果證明了在氮化鋁鎵/氮化鎵異質結構下，結構轉置不對偁是造成能階分裂的主因◦ 此外，我們在氮化鋁鎵/氮化鎵異質結構中亦做了微波調制的Shubnikov-de Hass磁性量測並且得到相同的結論 ◦ 然而，為了得到更完美的物理圖像，我們在同一塊樣品上做了旋光以及磁場下的測量◦ 經過定量的分析，我們可以將光學以及電學的實驗結果連結並做出合理的解釋◦ 再一次的我們證明了結構轉置不對偁是造成能階分裂的主因◦ 最後，我們探測了高場下電子的自旋行為，藉由Shubnikov-de Haas震盪的峰值分裂，我們可以估計不同藍道能階的g-係數大小 ◦ 實驗結果發現我們的測量值比一般塊材(bulk)的值來的大◦其原因來自於多體粒子之間交換能的增加所導致◦另一方面，g-係數會隨著藍道係數的減少而增大 ◦ 其原因在於比較少的藍道係數會對應到比較多的電子電子交互作用所導致 ◦Abstract We have investigated spin properties using optical (circular photogavinic effect) and transport measurement (Shubnikov-de Haas oscillations) in two-dimensional GaN electron systems. This dissertation contains the following parts. At the beginning, the circular photogalvanic effects (CPGE), induced by ultraviolet (325 nm) radiation, have been observed in the (0001)-oriented Al0.15Ga0.85N/GaN superlattices. The CPGE current changes sign upon reversing the radiation helicity, and it is up to two orders of magnitude larger than that obtained by far-infrared radiation. This result suggests the existence of a sizeable spin splitting in AlGaN/GaN superlattices. In order to detect the underlying mechanism behind spin splitting, low-temperature magnetotransport measurements were performed on AlGaN/GaN two-dimensional electron systems. By studying the beating pattern in the Shubnikov–de Haas oscillations in a perpendicular magnetic field, we are able to measure the zero-field spin-splitting energies in our systems. Our experimental results demonstrate that the Rashba term due to structural inversion asymmetry is the dominant mechanism which gives rise to the measured zero-field spin splitting in our wurzite AlGaN/GaN structures. In addition, to confirm our results, we also report zero-field spin splitting using microwave-modulated Shubnikov-de Hass (SdH) oscillations in an Al0.25Ga0.75N/GaN heterostructure and get the same conclusion. In order to obtain a unified physical picture, we compare CPGE and SdH measurements in the same sample. Both experiments are tested in (0001)-oriented Al0.25Ga0.75N/GaN heterostructures. Though a quantitative analysis, we establish the link between the beating of SdH oscillations and the CPGE. This shows that the underlying mechanism responsible for both phenomena is the Rashba effect. At last, we investigate spin in high magnetic regime. By measuring the positions of a pair of spin-split SdH maxima, we are able to estimate the g-factors at different Landau level (LL) indices. We find the g-factor is enhanced over its bulk value in GaN (~2) due to many-body exchange interactions. Moreover, the measured g-factor increases with decreasing LL index, indicating that many-body electron–electron interactions become stronger as the number of occupied LLs decreases.Contents Chapter 1 Introduction 1.1 Nitride-based semiconductors….……………………………………………….1 1.2 Crystal structure of GaN and AlN……………………...………………….……3 1.3 The modulation doped AlGaN/GaN heterostructure………….………….……..6 1.4 The spin splitting in AlGaN/GaN 2DEG systems….………………………….12 1.4.1 Spin-orbit interaction………………………………………...…………..12 1.4.2 Structure inversion asymmetry...................................................................13 1.4.3 Bulk inversion asymmetry..........................................................................17 1.5 Overview of this thesis…………….…………………………………….……..19 Chapter 2 Experiment 2.1 Sample preparation…………….……………………………….……………...22 2.2 Optical measurement………………….…………………..…………….……..26 2.3 Transport mearurement……………………………………………………...…28 Chapter 3 Theory 3.1 Photogalvinic effect…………………………………….…………………..….36 3.1.1 Circular photogalvinic effect (CPGE)…………………………………...36 3.1.1 Linear photogalvinic effect (LPGE)…………………………………......39 3.2 Basic concept of transport measurement……………………………………....42 3.2.1 Density of states………………………………………..………………..42 3.2.2 Landau levels and Shubnikov-de Haas oscillations……………………..46 3.2.3 Spin in high magnetic field…………………………………..……….….49 Chapter 4 The circular photogalvanic effects for inter-band absorption in AlGaN/GaN heterostructures 4.1 Introduction ……………………………………………………………..…....51 4.2 Experiment………………………………………………………….………....52 4.3 Results and discussion…………………………………..…………….…….....53 4.4 Summary………….……………………………………………………..….….59 Chapter 5 Zero-field spin splitting in modulation-doped AlxGa1–xN/GaN two-dimensional electron systems 5.1 Introduction ……………………………………………………………..….....62 5.2 Experiment………………………………………………………….………....63 5.3 Results and discussion…………………………………..…………….…….....64 5.4 Summary………….……………………………………………………..……..76 Chapter 6 Demonstration of Rashba spin splitting in an Al0.25Ga0.75N/GaN heterostructure by microwave-modulated Shubnikov-de Haas oscillations 6.1 Introduction ……………………………………………………………..….....79 6.2 Experiment………………………………………………………….………....80 6.3 Results and discussion…………………………………..…………….…….....81 6.4 Summary………….……………………………………………………..……..88 Chapter 7 Comparison CPGE effect with SdH oscillations in AlGaN/GaN single quantum well 7.1 Introduction ……………………………………………………………..….....90 7.2 Experiment………………………………………………………….………....91 7.3 Results and discussion…………………………………..…………….…….....91 7.4 Summary………….……………………………………………………..……102 Chapter 8 Exchange-Enhanced g-factors in an Al0.25Ga0.75N/GaN two-dimensional electron system 8.1 Introduction ……………………………………………………………..…...105 8.2 Experiment………………………………………………………….………..107 8.3 Results and discussion…………………………………..…………….……...107 8.4 Summary………….……………………………………………………..……118 Chapter 9 Discussion ………………………………………………………………….………….……….121 Chapter 10 Conclusion ....................................................................................................................................128 Lists of Figures Fig. 1.1 The diagrams show the wurtzite structure for Ga-face, N-face and the relation of the two lattice constants……………………….…….…………………....6 Fig. 1.2 The bandgaps of AlN, GaN, and InN as a function of lattice constants…...…7 Fig. 1.3 Schematic diagrams showing the sample structure (a) and band structure (b)………………………….…………………………………….………....12 Fig. 1.4 A Schematic 2D band structure with SIA called Rashba effect, the energy E(k) is plotted as a function of kx and ky………………..……………..….…..…17 Fig. 1.5 The simple picture of the conduction band structure (a) without spin-orbit coupling (b) with spin-orbit coupling…………………………...…….……18 Fig. 1.6 Schematic diagrams showing the zincblende structure…………….………..20 Fig. 2.1 The diagram shows the sample structure and the corresponding band structure.…………………….……….……………………………………26 Fig. 2.2 The diagram shows the sample structure and the corresponding band structure.………………………………………..…………………………27 Fig. 2.3 (a) shows the simple experiment setup which can result in circular polarization light. (b) is the simple experiment setup which can result in spin orientation current.………….……………………………….…....…29 Fig. 2.4 An Oxford Instruments top-loading He3 cryostat.….…………………….…31 Fig. 2.5 A diagram shows the operating principle of the He3 cryostat....................…32 Fig. 2.6 (a) is an Oxford Instruments He4 cryostat and (b) is the microwave generator.…………………………………………………………….…....35 Fig. 2.7 The setup of four-terminal resistance measurement..…………………….…36 Fig. 2.8 A schematic diagram showing the simple geometry of the microwave-modulated experiment. The inset below is the shape of the modulated microwave………………….…………………………….….…37 Fig. 3.1 (a) The transition without inversion asymmetry and circular polarization light. (b) The transition with circular polarization light but still without inversion asymmetry. (c) The microscopic picture describing the origin of spin current. The green arrows are the σ- transitions from s=3/2 heavy holes to s=1/2 electrons. Both σ+ and σ- cause unbalanced occupation in momentum space resulting in an electric current in real space..………………….……………..…………………………………...43 Fig. 3.2 Geometry used to calculate the density of states in (a) three dimensions, (b) two dimensions, and (c) one dimension.……………………………....…46 Fig. 3.3 Density of states N(E) as a function of energy E for 3D, 2D, and 1D systems..………….…………………………………………………....…47 Fig. 3.4 Schematic diagrams showing the energy levels of a two-dimensional system. (a) Without magnetic field. (b) Applying magnetic field in an ideal system. (c) Applying magnetic field in real case. (d) Schematic diagrams showing the oscillations in the density of states at the fixed Fermi energy with increasing the magnetic field..…………….………………….………..…...50 Fig. 4.1 The photocurrent in (0001)-grown AlGaN/GaN superlattices normalized by the radiation power P as a function of phase angle φ. The measurements are obtained at room temperature (T=300 K) for oblique incidence (Ф =600) by He-Cd laser at the wavelength 325 nm. The blue line is fitted using Eq. 4.1 which is a combination of the CPGE, LPGE and photovoltaic effect. The green-dash and red-dot lines show the oscillation current proportional to sin2φ and sin2φcos2φ, respectively.…………………………….…………58 Fig. 4.2 The photo-induced CPGE and LPGE currents in AlGaN/GaN superlattices normalized by the light power P at different incident angle (Ф)..……..…...59 Fig. 4.3 The temperature dependence of the photo-currents for the CPGE and LPGE in (0001)-grown AlGaN/GaN superlattices. The measurements are obtained for oblique incidence (Ф =600) by 325 nm laser …………………………..60 Fig. 5.1. Shubnikov–de Haas oscillations at the lowest temperature T=0.30 K for sample A. Inset (a) shows the sample structures and inset (b) shows the fast Fourier transform (FFT) spectrum of the data. …………………………..69 Fig. 5.2 Inverse magnetic-field (1/B) dependence of magnetoresistance Rxx at the temperature T=1.2 K for sample C before illumination (dot line) and after full illumination (dash–dot line). The insets show the corresponding FFT spectrum of the data………………………………………………………73 Fig. 5.3 The diagram shows the mechanism of illumination in the triangular well…76 Fig. 6.1 (a) Conventional Shubnikov-de Hass oscillations on the Al0.25Ga0.75N/GaN heterostructure at T=3.3 K. (b) The curve obtained by subtracting the background at T = 3.3 K……………………………………………….….86 Fig. 6.2 The microwave-modulated longitudinal magnetoresistivity as a function of the magnetic field is shown in (a). The pronounced beating curve is obtained by subtracting the background at T= 3.3 K. The frequency of the microwave is 2 GHz……………………..…………………………..……87 Fig. 6.3 Inverse magnetic-field (1/B) dependence of magnetoresistivity Rxx at the temperature T=3.3 K before and after illumination. The arrows indicate the position of beating nodes and the insets show the corresponding FFT spectrums of our data……………………………………………………...89 Fig. 7.1 (a) Shubnikov–de Haas oscillations at the lowest temperature T=0.3 K for sample A. The inset diagram shows the Hall measurement of sample A at T= 4.2 K. (b) The first derivative of the magnetoresistance Rxx for seeing clearer beating pattern. (c) The fast Fourier transform spectrum of the data………………………………………………………………………...97 Fig. 7.2 The original photocurrent in an (0001)-grown AlGaN/GaN heterostructure (sample A) normalized by the radiation power P as a function of phase angle φ with different incident angle Ф0. The red lines are the fitting curves using Eq. 4.1. The measurements are obtained at room temperature (T=300 K) by He-Cd laser at the wavelength λ = 325 nm.……………………..…98 Fig. 7.3 The fitting results of the CPGE and LPGE photocurrents in sample A normalized by the light power P as a function of the incident angle Ф0. The fitting curve in CPGE is according to Eq. 7.2…………………...……….103 Fig. 8.1. Magnetoresistance ρxx vs. magnetic field B data at the lowest temperature T = 0.30 K.........................................................................................................111 Fig. 8.2. Typical spin-split SdH oscillation data at various temperature range. From the top to bottom T = 6.66 K, 4.42 K, 3.52 K, 2.96 K, 1.53 K, 1.21 K, 0.79 K, 0.59 K and 0.30 K……………………...………………………….….112 Fig. 8.3. The energy difference ∆E between Fermi level EF and the subband minimum E0 against magnetic-field B………………………….…………………..116 Fig. 8.4. The effective g-factor as a function of Landau level index. Notice that there is a steady decrease of g-factor with increasing Landau level index…….117 Fig. 8.5. The double Gaussian fit shown in the dotted lines of the peaks in the vicinity of Landau level n=13. The dashed line is the sum of the two Gaussians...118 Lists of Tables Table 1.1. The properties of AlGaN/GaN heterostructures comparing with other materials………………………………………………………………13 Table 5.1. Parameters and measured zero-field spin-splitting factors for our AlxGa1–xN/GaN samples…………………..………………………..…71 Table 5.2. Parameters and measured zero-field spin-splitting factors for different illumination times in sample C…………………………....…………..74 Table 7.1. Fitting parameters vs incident angle Φ in our Al0.25Ga0.75N/GaN heterostructures………………………………………………………... 9