半导体空穴自旋弛豫及铁磁半导体Landau-Lifshitz-Gilbert方程的理论研究
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摘要
自旋电子学是一门以固体材料中电子的自旋自由度作为信息载体与研究对象的学科,其中一个重要的分支为半导体自旋电子学。半导体自旋电子学涉及到半导体中自旋极化的产生、维持、操控以及探测等多个方面,而自旋极化的动力学性质对这些目标的实现都是十分关键的。本论文主要讨论Ⅲ-V族半导体以及由其衍生的铁磁半导体中体材料的动力学性质,具体包括Ⅲ-V族半导体中的g因子、载流子自旋弛豫时间以及铁磁半导体的载流子自旋寿命和磁矩运动方程等。
我们首先概述了自旋电子学的背景并简单回顾了文献中对半导体中电子自旋弛豫的研究,然后仔细介绍了半导体中空穴自旋弛豫的实验与理论方面研究进展。接着,我们介绍了铁磁半导体中的能带理论、超快动力学研究以及理论上描述磁矩演化的Landau-Lifshitz-Gilbert方程的发展,并重点介绍了方程中的Gilbert阻尼系数以及非绝热参数的理论研究。
在论文的第二章中,我们讨论了一些常见半导体材料中不同能谷的自旋轨道耦合与9因子。我们用k·p理论得到自旋轨道耦合形式并比较文献中用k·p理论、紧束缚模型以及第一性原理计算等方法确定的常见Ⅲ-V族半导体材料的自旋轨道耦合系数。此外,我们还介绍用k·p理论计算9因子的方法并在第三章中利用这种方法计算了闪锌矿结构GaAs与AlAs体材料中最低导带L谷以及GaN中最低导带X谷的9因子。我们发现GaAs与AlAs的L谷g因子具有明显的各向异性,而GaN的X谷g因子则基本是各向同性的。其中X谷的9因子数值与L谷的横向9因子都近似等于自由电子9因子。接着我们利用sp3d5s*紧束缚模型计算导带自旋劈裂,从而得到GaN中X谷的自旋轨道耦合系数0.29eVA,它比用sp3s*模型得到的结果要大一个量级。
第四章中,我们首先给出了半导体体材料中的动力学自旋Bloch方程。我们通过分析导带、价带之间的耦合并结合collinear表象与helix表象之间的变换解释了D'yakonov-Perel'与Elliott-Yafet两种电子自旋弛豫机制的来源,并介绍了引起Bir-Aronov-Pikus自旋弛豫的电子-空穴自旋交换散射项。对于空穴系统,考虑到费米面附近轻、重空穴之间的能量劈裂,我们忽略轻、重空穴之间的关联,把helix表象的运动方程约化成关于轻、重空穴两部分密度矩阵的形式。我们把这种做法下由散射项直接导致的自旋弛豫统一归为空穴的Elliott-Yafet自旋弛豫机制,而把依赖于轻、重空穴带自旋进动的自旋弛豫过程称为D'yakonov-Perel'自旋弛豫过程。
从第五章到第八章,我们利用动力学自旋Bloch方程方法具体研究GaAs与铁磁GaMnAs体材料中的自旋／磁矩动力学性质。在第五章中,我们分析了实验上测得的n型材料电子自旋弛豫时间在低温下的浓度关系。通过计算光激发导致的热电子效应,我们证实实验上观测到的弛豫时间极大值是由简并、非简并极限的过渡导致的,与此前的理论预言一致。
第六章,我们利用动力学自旋Bloch方程研究了本征型与p型GaAs体材料中的空穴自旋弛豫。在我们的计算中包含了诸如空穴-杂质、空穴-声子、空穴-电子以及空穴-空穴等所有相关的散射。由于波函数与自旋劈裂能量都由对角化Kane哈密顿量得到,因此我们可以较为准确的描述波函数混合引起的Elliott-Yafet自旋弛豫以及由自旋进动引起的D'yakonov-Perel'自旋弛豫的贡献。我们发现Elliott-Yafet机制始终是空穴的主要自旋弛豫机制,这与价带自身的强自旋轨道耦合有关。在本征材料中,我们在室温下得到的空穴自旋弛豫时间为110fs左右,与之前的实验结果符合得很好。我们的计算结果表明以往文献中遗漏的轻、重空穴的带内自旋关联(helix表象密度矩阵的非对角项)以及空穴与光学声子的非极化相互作用都是十分重要的。进一步,我们仔细讨论了不同温度、浓度下的空穴自旋弛豫时间。我们发现随着温度降低,空穴的自旋弛豫时间可能延长一个量级以上。我们发现自旋弛豫时间在高温下随浓度上升单调下降,而低温下却呈现先上升后下降的非单调行为,这与库仑散射在简并、非简并极限下的不同行为有关。在p型材料的研究中,我们也预言了空穴自旋弛豫时间丰富的非单调温度、浓度依赖关系。我们发现这种非单调性主要由杂质散射强度变化引起并且受到屏蔽的影响,而在高温下电声散射也会有比较重要的贡献。
在第七章中,我们基于s-d交换模型推导了铁磁半导体中的Landau-Lifshitz-Gilbert方程。我们把巡游电子的自旋轴取成局域、瞬时的磁矩方向,从而引入了自旋态之间的规范场耦合。在包含规范场相互作用的情况下,我们用非平衡格林函数方法推导了巡游电子动力学自旋Bloch方程,并在弛豫时间近似下通过求解方程得到巡游电子自旋极化对局域电子磁矩的自旋扭矩作用。在空间均匀体系中,我们发现除了自旋翻转散射以外,自旋守恒散射也会通过D'yakonov-Perel'自旋弛豫机制对巡游电子的自旋弛豫时间产生修正进而影响Gilbert阻尼扭矩,并且空间均匀的自旋流在自旋轨道耦合的作用下也会对Gilbert阻尼产生贡献。当磁矩存在空间梯度时,一阶梯度项给出正比于自旋流大小的自旋扭矩,它包括直接的自旋交换扭矩以及正比于非绝热参数的横向自旋交换扭矩,与之前文献中的结果一致。在二阶梯度下,我们得到了两项有效磁场贡献,其中一项为常规的自旋刚度项,而另外一项贡献同时垂直于常规自旋刚度与磁矩方向。我们发现这项垂直自旋刚度会导致磁畴壁偏离理想的Neel结构而出现螺旋形结构。由于铁磁半导体中的非绝热参数较大,垂直自旋刚度会比较重要。
接着我们在第八章中用实际样品参数具体计算了GaMnAs中Landau-Lifshitz-Gilbert方程中的系数。由于这些系数都与载流子的自旋寿命有关,因此我们首先利用Zener模型通过数值求解动力学方程计算了铁磁相GaMnAs中的空穴自旋弛豫时间。由于空穴始终处于强简并极限下,因此我们在计算中忽略了库仑散射,温度效应通过磁矩Brillouin函数引入。从我们的计算结果来看,在p-d交换系数比较小的情况下,空穴的自旋弛豫时间随温度上升而单调下降,而在交换系数比较大的时候,空穴自旋弛豫时间先上升后下降。通过分析我们发现这种现象的产生与空穴带之间的波函数混合随Zeeman劈裂的变化有关。我们把空穴自旋弛豫时间代入到LLG系数的解析表达式中,得到的低温非绝热参数β在0.3左右,与实验值一致。随着温度升高到居里温度附近,非绝热参数显著增大并可以超过1。在β<1的区域,我们得到的Gilbert阻尼系数随着温度上升缓慢上升,数值以及温度关系都与实验观测相符。在β>1的区域,我们预言阻尼系数随温度上升而下降。此外,我们也计算了自旋刚度系数与垂直自旋刚度系数。我们发现垂直自旋刚度系数也会和阻尼系数一样呈现非单调行为。
我们在第九章中仔细讨论了等间距的π脉冲序列对(001)GaAs量子阱中电子自旋弛豫的影响。在包含所有相关散射的情况下,我们发现脉冲间距超过40ps时强、弱散射极限下的自旋弛豫时间基本都不受脉冲间距的影响。随着脉冲间距缩短,电子的自旋弛豫时间可以显著延长。计算结果表明自旋弛豫时间的温度、浓度依赖关系与动量弛豫时间基本一致,这是因为密集的π脉冲成为抑制有效磁场非均匀扩展的主要机制而散射的主要作用则是提供自旋弛豫通道。我们发现在高迁移率、低温、高／低电子浓度条件下,π脉冲序列对自旋弛豫时间的调节效果最强。
最后我们还在第十章中介绍了一种在介观尺度基于局域Rashba自旋轨道耦合设计的T形自旋晶体管模型。这种模型通过把Fano-Rashba效应与T形结构波导管的结构反共振结合起来,利用Fano反共振点与结构反共振点相靠近时造成的带隙来减小器件关闭状态的漏电流。与依靠单独的Fano反共振点或结构反共振点设计的晶体管相比,我们的设计方案极大地提高了器件的皮实性。
Semiconductor spintronics is an important branch in spintronics, which is based on the usage of the spin degree of freedom in solid state materials. Investigations on this field involve the generation, storage, manipulation and detection of spin polarization in semiconductors, where the spin dynamic properties are quite essential. This dissertation focuses on the dynamic properties in bulk III-V semiconductors and ferromagnetic semi-conductors, including the g-factor, spin relaxation time and the dynamic equation of the magnetization in semiconductors and/or ferromagnetic semiconductors.
We first give a brief review on the background of the spintronics and the studies on the electron spin relaxation in III-V semiconductors in the literature. Then we explicitly intro-duce both experimetal and theoretical works on the hole spin relaxation in semiconductors. We also introduce the band-structure theory and ultrafast dynamics study in ferromag-netic semiconductors. Moreover, the development of the Landau-Lifshitz-Gilbert equation and the theoretical derivation on the Gilbert damping and non-adiabatic parameters are also introduced in the first chapter.
In Chapter II, we discuss the spin-orbit coupling and g-factor in different valleys and different materials. We derive the spin-orbit coupling from the k-p theory and compare the coupling coefficients obtained from the k· p theory, tight-binding model and first principle calculation in the literature. Moreover, we also introduce the approach to calculate the g factor from the k· p theory, which we employ to study the L and X valleys in zincblende III-V semiconductors in Chapter III. The g factors of the L valley in GaAs and AlAs show significant anisotropy, while that of the X valley in GaN is almost isotropic. We find that the g factor of the X valley and the transverse component of the L valley are both close to the free electron g factor. In addition, we obtain the spin-orbit coupling coefficient of the X valley in GaN by calculating the spin splitting of the conduction band from the tight-binding models. The value from the sp3d5s*model is about0.29eVA, which is one order of magnitude larger than that from sp3s*.
In Chapter IV, we first introduce the kinetic spin Bloch equations in semiconductor and explain the origin of the D'yakonov-Perel'and Elliott-Yafet mechanisms during the electron spin relaxation, by analyzing the coupling between the conduction and valence bands in the transformation between the collinear and helix representations. We also show the electron-hole exchange scattering term, which leads to the Bir-Aronov-Pikus spin relaxation mechanism, in the kinetic spin Bloch equations. By taking into account the large energy splitting between the light-and heavy-hole bands, we neglect all the interband coherence in the kinetic spin Bloch equations. Under this technique, the spin relaxation of hole gas solely due to the scatterings is attributed to the Elliott-Yafet mechanism, and that associated with the spin precession is referred as the D'yakonov-Perel'mechanism.
From Chapter Ⅴ to Ⅷ, we study the spin dynamic properties in bulk GaAs and ferromagnetic GaMnAs. We first analyze the nonmonotonic doping-density dependence of the electron spin relaxation time observed in n-type GaAs at low temperature. By taking into account the laser-induced hot-electron effect, we confirm that the peak of the spin relaxation time is nothing but the consequence of the crossover between the degenerate and the non-degenerate limits.
By employing the kinetic spin Bloch equations, we investigate the hole spin relaxation in both intrinsic and p-type bulk GaAs in Chapter Ⅵ. In our calculation, we include all the relevant scatterings, such as the hole-impurity, hole-phonon, hole-electron and hole-hole scatterings. We obtain the wave functions and spin splitting energies exactly from the Kane Hamiltonian, which allows us to determine the contributions from both the Elliott-Yafet and D'yakonov-Perel'mechanisms. We find that, due to the strong spin-orbit coupling, the Elliott-Yafet mechanism is always dominant during the hole spin relaxation. In the intrinsic case, the hole spin relaxation time is about110fs at room temperature, which agrees well with experiment. We show that the nonpolar hole-optical-phonon scattering and the spin coherence components between the two heavy-hole bands as well as light-hole bands, which were missed in the previous studies on the hole spin dynamics, both are very important. Further, we explicitly discuss the temperature and density dependences of the hole spin relaxation time. We find that the hole spin relaxation time can be extended by one order of magnitude as the temperature decreases. Moreover, we predict that the hole spin relaxation time decreases with increasing the density at high temperature, while a nonmonotonic density dependence appears. We show that the nonmonotonic density dependence of the hole spin relaxation time results from the different behaviors of the Coulomb scattering in the degenerate and non-degenerate limits. In the p-type case, we also predict rich nonmonotonic features in the temperature and density dependences of the hole spin relaxation time, which result from the variation of the hole-impurity and hole-phonon scattering strength. The screening is found to play an important role in the hole-impurity scattering.
In Chapter Ⅶ, we derive the Landau-Lifshitz-Gilbert equation based on the s-d ex-change model in ferromagnetic semiconductors, where we define the spin operators under the local and instantaneous magnetization orientation hence introduce the spin couplings through the gauge field. By employing the non-equilibrium Green's-function approach, we derive the kinetic spin Bloch equations of the itinerant carriers from the Hamiltonian with the gauge field. Under the relaxation time approximation, we solve the kinetic spin Bloch equations and calculate the spin torque of the magnetization due to the itinerant electron spin polarization. In the spatially homogeneous system, we show that the spin-conserving scattering as well as the spin-flip scattering can contribute to the electron spin relaxation time through the D'yakonov-Perel' mechanism, hence correct the Gilbert damping torque. Moreover, the spatially homogeneous spin current is also found to contribute to the Gilbert damping coefficient in the presence of spin-orbit coupling. In the inhomogeneous case, the first-order gradient of the magnetization leads to two spin transfer torques, the transverse mode of which is proportional to the non-adiabatic parameter. At the second-order gra-dient, we obtain two effective magnetic fields. One is the conventional spin stiffness term, while the other, the vertical spin stiffness, is perpendicular to both the spin stiffness and magnetization. We show that the vertical spin stiffness makes the domain wall violate the ideal Neel wall structure, resulting in a spiral feature. Since the non-adiabatic parameter is large in ferromagnetic semiconductors, the vertical spin stiffness can be important.
Further, we calculate the coefficients in the Landau-Lifshitz-Gilbert equation by us-ing the parameters in GaMnAs samples in experiments. Since these coefficients are all dependent on the carrier spin lifetime, we first calculate the hole spin relaxation time by numerically solving the kinetic equations under the Zener model. In the calculation, we neglect the Coulomb scattering due to the strong degenerate condition of the hole gas in all cases. The temperature effect is introduced through the temperature dependence of the magnetization following the Brillouin function. We show that, as the temperature increases, the hole spin relaxation time monotonically decreases for a small p-d exchange coefficient, while it first increases then decreases for the strong p-d exchange case. We analyze the nonmonotonic phenomenon and conclude that it originates from the variation of the inter-band spin mixing while the Zeeman splitting changes. We then substitute the hole spin relaxation time into the analytical expressions of the Landau-Lifshitz-Gilbert coefficients. We find that the non-adiabatic parameter β is around0.3, which shows good agreement with the experiment. As the temperature approaches to the Curie temperature, the non-adiabatic parameter increases and can even exceed one. In the regime with β<1, the Gilbert damping coefficient gradually increases with increasing temperature, which is consistent with the experiments. In the regime with β>1, we predict a decrease of the Gilbert damping coefficient with increasing temperature. Moreover, we also calculate the temperature dependence of the spin stiffness and vertical spin stiffness coefficients, where the latter also shows a nonmonotonic feature.
Furthermore, we explicitly analyze the influence of a serried7r-pulse spin rephasing sequence on the electron spin relaxation in (001) GaAs quantum wells. We find that the spin relaxation time is only slightly affected by the pulses, both in the strong and weak scattering limits, when the inter-pulse spacing is larger than40ps. As the inter-pulse spacing decreases, the electron spin relaxation time can be significantly extended. We show that the temperature and density dependences of the spin relaxation time are consistent with those of the momentum scattering time. The reason lies in the fact that, under the serried π-pulse sequence, the inhomogeneous broadening is mainly suppressed by the pulses, and the scattering mainly performs as the source of the spin relaxation channel. According to our results, the efficient manipulation of the spin lifetime through the π-pulse rephasing sequence requires high mobility samples with very low (or high) electron densities and low temperature.
Finally, we propose a spin transistor model at the mesoscopic level, which is based on a T-shaped waveguide with local Rashba spin-orbit coupling. By combining the Fano-Rashba effect and the structure antiresonance due to the geometry of the waveguide, we show that there would be a wide energy gap on the transmission curve when the Fano an-tiresonance and structure antiresonance points are tuned to be close to each other. Hence, the leakage current in the gap is rather small. We show that our spin transistor is of better robustness than those based on a single Fano antiresonance or structure antiresonance.
我们首先概述了自旋电子学的背景并简单回顾了文献中对半导体中电子自旋弛豫的研究,然后仔细介绍了半导体中空穴自旋弛豫的实验与理论方面研究进展。接着,我们介绍了铁磁半导体中的能带理论、超快动力学研究以及理论上描述磁矩演化的Landau-Lifshitz-Gilbert方程的发展,并重点介绍了方程中的Gilbert阻尼系数以及非绝热参数的理论研究。
在论文的第二章中,我们讨论了一些常见半导体材料中不同能谷的自旋轨道耦合与9因子。我们用k·p理论得到自旋轨道耦合形式并比较文献中用k·p理论、紧束缚模型以及第一性原理计算等方法确定的常见Ⅲ-V族半导体材料的自旋轨道耦合系数。此外,我们还介绍用k·p理论计算9因子的方法并在第三章中利用这种方法计算了闪锌矿结构GaAs与AlAs体材料中最低导带L谷以及GaN中最低导带X谷的9因子。我们发现GaAs与AlAs的L谷g因子具有明显的各向异性,而GaN的X谷g因子则基本是各向同性的。其中X谷的9因子数值与L谷的横向9因子都近似等于自由电子9因子。接着我们利用sp3d5s*紧束缚模型计算导带自旋劈裂,从而得到GaN中X谷的自旋轨道耦合系数0.29eVA,它比用sp3s*模型得到的结果要大一个量级。
第四章中,我们首先给出了半导体体材料中的动力学自旋Bloch方程。我们通过分析导带、价带之间的耦合并结合collinear表象与helix表象之间的变换解释了D'yakonov-Perel'与Elliott-Yafet两种电子自旋弛豫机制的来源,并介绍了引起Bir-Aronov-Pikus自旋弛豫的电子-空穴自旋交换散射项。对于空穴系统,考虑到费米面附近轻、重空穴之间的能量劈裂,我们忽略轻、重空穴之间的关联,把helix表象的运动方程约化成关于轻、重空穴两部分密度矩阵的形式。我们把这种做法下由散射项直接导致的自旋弛豫统一归为空穴的Elliott-Yafet自旋弛豫机制,而把依赖于轻、重空穴带自旋进动的自旋弛豫过程称为D'yakonov-Perel'自旋弛豫过程。
从第五章到第八章,我们利用动力学自旋Bloch方程方法具体研究GaAs与铁磁GaMnAs体材料中的自旋／磁矩动力学性质。在第五章中,我们分析了实验上测得的n型材料电子自旋弛豫时间在低温下的浓度关系。通过计算光激发导致的热电子效应,我们证实实验上观测到的弛豫时间极大值是由简并、非简并极限的过渡导致的,与此前的理论预言一致。
第六章,我们利用动力学自旋Bloch方程研究了本征型与p型GaAs体材料中的空穴自旋弛豫。在我们的计算中包含了诸如空穴-杂质、空穴-声子、空穴-电子以及空穴-空穴等所有相关的散射。由于波函数与自旋劈裂能量都由对角化Kane哈密顿量得到,因此我们可以较为准确的描述波函数混合引起的Elliott-Yafet自旋弛豫以及由自旋进动引起的D'yakonov-Perel'自旋弛豫的贡献。我们发现Elliott-Yafet机制始终是空穴的主要自旋弛豫机制,这与价带自身的强自旋轨道耦合有关。在本征材料中,我们在室温下得到的空穴自旋弛豫时间为110fs左右,与之前的实验结果符合得很好。我们的计算结果表明以往文献中遗漏的轻、重空穴的带内自旋关联(helix表象密度矩阵的非对角项)以及空穴与光学声子的非极化相互作用都是十分重要的。进一步,我们仔细讨论了不同温度、浓度下的空穴自旋弛豫时间。我们发现随着温度降低,空穴的自旋弛豫时间可能延长一个量级以上。我们发现自旋弛豫时间在高温下随浓度上升单调下降,而低温下却呈现先上升后下降的非单调行为,这与库仑散射在简并、非简并极限下的不同行为有关。在p型材料的研究中,我们也预言了空穴自旋弛豫时间丰富的非单调温度、浓度依赖关系。我们发现这种非单调性主要由杂质散射强度变化引起并且受到屏蔽的影响,而在高温下电声散射也会有比较重要的贡献。
在第七章中,我们基于s-d交换模型推导了铁磁半导体中的Landau-Lifshitz-Gilbert方程。我们把巡游电子的自旋轴取成局域、瞬时的磁矩方向,从而引入了自旋态之间的规范场耦合。在包含规范场相互作用的情况下,我们用非平衡格林函数方法推导了巡游电子动力学自旋Bloch方程,并在弛豫时间近似下通过求解方程得到巡游电子自旋极化对局域电子磁矩的自旋扭矩作用。在空间均匀体系中,我们发现除了自旋翻转散射以外,自旋守恒散射也会通过D'yakonov-Perel'自旋弛豫机制对巡游电子的自旋弛豫时间产生修正进而影响Gilbert阻尼扭矩,并且空间均匀的自旋流在自旋轨道耦合的作用下也会对Gilbert阻尼产生贡献。当磁矩存在空间梯度时,一阶梯度项给出正比于自旋流大小的自旋扭矩,它包括直接的自旋交换扭矩以及正比于非绝热参数的横向自旋交换扭矩,与之前文献中的结果一致。在二阶梯度下,我们得到了两项有效磁场贡献,其中一项为常规的自旋刚度项,而另外一项贡献同时垂直于常规自旋刚度与磁矩方向。我们发现这项垂直自旋刚度会导致磁畴壁偏离理想的Neel结构而出现螺旋形结构。由于铁磁半导体中的非绝热参数较大,垂直自旋刚度会比较重要。
接着我们在第八章中用实际样品参数具体计算了GaMnAs中Landau-Lifshitz-Gilbert方程中的系数。由于这些系数都与载流子的自旋寿命有关,因此我们首先利用Zener模型通过数值求解动力学方程计算了铁磁相GaMnAs中的空穴自旋弛豫时间。由于空穴始终处于强简并极限下,因此我们在计算中忽略了库仑散射,温度效应通过磁矩Brillouin函数引入。从我们的计算结果来看,在p-d交换系数比较小的情况下,空穴的自旋弛豫时间随温度上升而单调下降,而在交换系数比较大的时候,空穴自旋弛豫时间先上升后下降。通过分析我们发现这种现象的产生与空穴带之间的波函数混合随Zeeman劈裂的变化有关。我们把空穴自旋弛豫时间代入到LLG系数的解析表达式中,得到的低温非绝热参数β在0.3左右,与实验值一致。随着温度升高到居里温度附近,非绝热参数显著增大并可以超过1。在β<1的区域,我们得到的Gilbert阻尼系数随着温度上升缓慢上升,数值以及温度关系都与实验观测相符。在β>1的区域,我们预言阻尼系数随温度上升而下降。此外,我们也计算了自旋刚度系数与垂直自旋刚度系数。我们发现垂直自旋刚度系数也会和阻尼系数一样呈现非单调行为。
我们在第九章中仔细讨论了等间距的π脉冲序列对(001)GaAs量子阱中电子自旋弛豫的影响。在包含所有相关散射的情况下,我们发现脉冲间距超过40ps时强、弱散射极限下的自旋弛豫时间基本都不受脉冲间距的影响。随着脉冲间距缩短,电子的自旋弛豫时间可以显著延长。计算结果表明自旋弛豫时间的温度、浓度依赖关系与动量弛豫时间基本一致,这是因为密集的π脉冲成为抑制有效磁场非均匀扩展的主要机制而散射的主要作用则是提供自旋弛豫通道。我们发现在高迁移率、低温、高／低电子浓度条件下,π脉冲序列对自旋弛豫时间的调节效果最强。
最后我们还在第十章中介绍了一种在介观尺度基于局域Rashba自旋轨道耦合设计的T形自旋晶体管模型。这种模型通过把Fano-Rashba效应与T形结构波导管的结构反共振结合起来,利用Fano反共振点与结构反共振点相靠近时造成的带隙来减小器件关闭状态的漏电流。与依靠单独的Fano反共振点或结构反共振点设计的晶体管相比,我们的设计方案极大地提高了器件的皮实性。
Semiconductor spintronics is an important branch in spintronics, which is based on the usage of the spin degree of freedom in solid state materials. Investigations on this field involve the generation, storage, manipulation and detection of spin polarization in semiconductors, where the spin dynamic properties are quite essential. This dissertation focuses on the dynamic properties in bulk III-V semiconductors and ferromagnetic semi-conductors, including the g-factor, spin relaxation time and the dynamic equation of the magnetization in semiconductors and/or ferromagnetic semiconductors.
We first give a brief review on the background of the spintronics and the studies on the electron spin relaxation in III-V semiconductors in the literature. Then we explicitly intro-duce both experimetal and theoretical works on the hole spin relaxation in semiconductors. We also introduce the band-structure theory and ultrafast dynamics study in ferromag-netic semiconductors. Moreover, the development of the Landau-Lifshitz-Gilbert equation and the theoretical derivation on the Gilbert damping and non-adiabatic parameters are also introduced in the first chapter.
In Chapter II, we discuss the spin-orbit coupling and g-factor in different valleys and different materials. We derive the spin-orbit coupling from the k-p theory and compare the coupling coefficients obtained from the k· p theory, tight-binding model and first principle calculation in the literature. Moreover, we also introduce the approach to calculate the g factor from the k· p theory, which we employ to study the L and X valleys in zincblende III-V semiconductors in Chapter III. The g factors of the L valley in GaAs and AlAs show significant anisotropy, while that of the X valley in GaN is almost isotropic. We find that the g factor of the X valley and the transverse component of the L valley are both close to the free electron g factor. In addition, we obtain the spin-orbit coupling coefficient of the X valley in GaN by calculating the spin splitting of the conduction band from the tight-binding models. The value from the sp3d5s*model is about0.29eVA, which is one order of magnitude larger than that from sp3s*.
In Chapter IV, we first introduce the kinetic spin Bloch equations in semiconductor and explain the origin of the D'yakonov-Perel'and Elliott-Yafet mechanisms during the electron spin relaxation, by analyzing the coupling between the conduction and valence bands in the transformation between the collinear and helix representations. We also show the electron-hole exchange scattering term, which leads to the Bir-Aronov-Pikus spin relaxation mechanism, in the kinetic spin Bloch equations. By taking into account the large energy splitting between the light-and heavy-hole bands, we neglect all the interband coherence in the kinetic spin Bloch equations. Under this technique, the spin relaxation of hole gas solely due to the scatterings is attributed to the Elliott-Yafet mechanism, and that associated with the spin precession is referred as the D'yakonov-Perel'mechanism.
From Chapter Ⅴ to Ⅷ, we study the spin dynamic properties in bulk GaAs and ferromagnetic GaMnAs. We first analyze the nonmonotonic doping-density dependence of the electron spin relaxation time observed in n-type GaAs at low temperature. By taking into account the laser-induced hot-electron effect, we confirm that the peak of the spin relaxation time is nothing but the consequence of the crossover between the degenerate and the non-degenerate limits.
By employing the kinetic spin Bloch equations, we investigate the hole spin relaxation in both intrinsic and p-type bulk GaAs in Chapter Ⅵ. In our calculation, we include all the relevant scatterings, such as the hole-impurity, hole-phonon, hole-electron and hole-hole scatterings. We obtain the wave functions and spin splitting energies exactly from the Kane Hamiltonian, which allows us to determine the contributions from both the Elliott-Yafet and D'yakonov-Perel'mechanisms. We find that, due to the strong spin-orbit coupling, the Elliott-Yafet mechanism is always dominant during the hole spin relaxation. In the intrinsic case, the hole spin relaxation time is about110fs at room temperature, which agrees well with experiment. We show that the nonpolar hole-optical-phonon scattering and the spin coherence components between the two heavy-hole bands as well as light-hole bands, which were missed in the previous studies on the hole spin dynamics, both are very important. Further, we explicitly discuss the temperature and density dependences of the hole spin relaxation time. We find that the hole spin relaxation time can be extended by one order of magnitude as the temperature decreases. Moreover, we predict that the hole spin relaxation time decreases with increasing the density at high temperature, while a nonmonotonic density dependence appears. We show that the nonmonotonic density dependence of the hole spin relaxation time results from the different behaviors of the Coulomb scattering in the degenerate and non-degenerate limits. In the p-type case, we also predict rich nonmonotonic features in the temperature and density dependences of the hole spin relaxation time, which result from the variation of the hole-impurity and hole-phonon scattering strength. The screening is found to play an important role in the hole-impurity scattering.
In Chapter Ⅶ, we derive the Landau-Lifshitz-Gilbert equation based on the s-d ex-change model in ferromagnetic semiconductors, where we define the spin operators under the local and instantaneous magnetization orientation hence introduce the spin couplings through the gauge field. By employing the non-equilibrium Green's-function approach, we derive the kinetic spin Bloch equations of the itinerant carriers from the Hamiltonian with the gauge field. Under the relaxation time approximation, we solve the kinetic spin Bloch equations and calculate the spin torque of the magnetization due to the itinerant electron spin polarization. In the spatially homogeneous system, we show that the spin-conserving scattering as well as the spin-flip scattering can contribute to the electron spin relaxation time through the D'yakonov-Perel' mechanism, hence correct the Gilbert damping torque. Moreover, the spatially homogeneous spin current is also found to contribute to the Gilbert damping coefficient in the presence of spin-orbit coupling. In the inhomogeneous case, the first-order gradient of the magnetization leads to two spin transfer torques, the transverse mode of which is proportional to the non-adiabatic parameter. At the second-order gra-dient, we obtain two effective magnetic fields. One is the conventional spin stiffness term, while the other, the vertical spin stiffness, is perpendicular to both the spin stiffness and magnetization. We show that the vertical spin stiffness makes the domain wall violate the ideal Neel wall structure, resulting in a spiral feature. Since the non-adiabatic parameter is large in ferromagnetic semiconductors, the vertical spin stiffness can be important.
Further, we calculate the coefficients in the Landau-Lifshitz-Gilbert equation by us-ing the parameters in GaMnAs samples in experiments. Since these coefficients are all dependent on the carrier spin lifetime, we first calculate the hole spin relaxation time by numerically solving the kinetic equations under the Zener model. In the calculation, we neglect the Coulomb scattering due to the strong degenerate condition of the hole gas in all cases. The temperature effect is introduced through the temperature dependence of the magnetization following the Brillouin function. We show that, as the temperature increases, the hole spin relaxation time monotonically decreases for a small p-d exchange coefficient, while it first increases then decreases for the strong p-d exchange case. We analyze the nonmonotonic phenomenon and conclude that it originates from the variation of the inter-band spin mixing while the Zeeman splitting changes. We then substitute the hole spin relaxation time into the analytical expressions of the Landau-Lifshitz-Gilbert coefficients. We find that the non-adiabatic parameter β is around0.3, which shows good agreement with the experiment. As the temperature approaches to the Curie temperature, the non-adiabatic parameter increases and can even exceed one. In the regime with β<1, the Gilbert damping coefficient gradually increases with increasing temperature, which is consistent with the experiments. In the regime with β>1, we predict a decrease of the Gilbert damping coefficient with increasing temperature. Moreover, we also calculate the temperature dependence of the spin stiffness and vertical spin stiffness coefficients, where the latter also shows a nonmonotonic feature.
Furthermore, we explicitly analyze the influence of a serried7r-pulse spin rephasing sequence on the electron spin relaxation in (001) GaAs quantum wells. We find that the spin relaxation time is only slightly affected by the pulses, both in the strong and weak scattering limits, when the inter-pulse spacing is larger than40ps. As the inter-pulse spacing decreases, the electron spin relaxation time can be significantly extended. We show that the temperature and density dependences of the spin relaxation time are consistent with those of the momentum scattering time. The reason lies in the fact that, under the serried π-pulse sequence, the inhomogeneous broadening is mainly suppressed by the pulses, and the scattering mainly performs as the source of the spin relaxation channel. According to our results, the efficient manipulation of the spin lifetime through the π-pulse rephasing sequence requires high mobility samples with very low (or high) electron densities and low temperature.
Finally, we propose a spin transistor model at the mesoscopic level, which is based on a T-shaped waveguide with local Rashba spin-orbit coupling. By combining the Fano-Rashba effect and the structure antiresonance due to the geometry of the waveguide, we show that there would be a wide energy gap on the transmission curve when the Fano an-tiresonance and structure antiresonance points are tuned to be close to each other. Hence, the leakage current in the gap is rather small. We show that our spin transistor is of better robustness than those based on a single Fano antiresonance or structure antiresonance.
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