Hole spin relaxation in [001] strained asymmetric Si/SiGe and Ge/SiGe quantum wells
Hole spin relaxation in [001] strained asymmetric Si/SiGe and Ge/SiGe quantum wells
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DOI：
10.1103/physrevb.80.155311
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发表时间：
2009-06
影响因子：
3.7
通讯作者：
P. Zhang;M. W. Wu
中科院分区：
文献类型：
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作者：
P. Zhang;M. W. Wu
研究了[001]应变不对称$\text{Si}/{\text{Si}}_{0.7}{\text{Ge}}_{0.3}$ $(\text{Ge}/{\text{Si}}_{0.3}{\text{Ge}}_{0.7})$量子阱中空穴的自旋弛豫。在包含充分基函数的六波段Luttinger $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$模型框架下，采用子带L\ owdin摄动法得到了最低空穴子带的有效哈密顿量。Si/SiGe量子阱的最低空穴子带为光空穴态，且Rashba自旋轨道耦合项与动量呈线性和三次关系，而Ge/SiGe量子阱的最低空穴子带为重空穴态，且Rashba自旋轨道耦合项仅与动量呈三次关系。采用考虑所有相关散射的全微观动力学自旋布洛赫方程方法研究了空穴自旋弛豫。发现空穴-声子散射非常弱，这使得空穴-空穴库仑散射变得非常重要。Si/SiGe量子阱中的空穴系统一般处于强散射极限，而Ge/SiGe量子阱中的空穴系统可以处于强散射极限，也可以处于弱散射极限。在Si/SiGe量子阱中，库仑散射导致自旋弛豫时间的温度依赖性和空穴密度依赖性都达到峰值，该峰值位于简并态和非简并态的交点附近。然而，在Ge/SiGe量子阱中，库仑散射导致自旋弛豫时间的温度依赖性不仅有峰，而且有谷。谷实际上是由于从弱散射极限到强散射极限的交叉。空穴杂质散射有效地影响了自旋弛豫。在强（弱）散射极限下，自旋弛豫时间随杂质密度的增大而增大（减小）。对于我们所考虑的温度、载流子/杂质密度和栅极电压，在Si/SiGe （Ge/SiGe）量子阱中，发现自旋弛豫时间为$1\ensuremath{\sim}100\text{ps}$ $(0.1\ensuremath{\sim}10\text{}\text{ps})$。
Hole spin relaxation in [001] strained asymmetric $\text{Si}/{\text{Si}}_{0.7}{\text{Ge}}_{0.3}$ $(\text{Ge}/{\text{Si}}_{0.3}{\text{Ge}}_{0.7})$ quantum wells is investigated in the situation with only the lowest hole subband being relevant. The effective Hamiltonian of the lowest hole subband is obtained by the subband L\"owdin perturbation method in the framework of the six-band Luttinger $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model with sufficient basis functions included. The lowest hole subband in Si/SiGe quantum wells is light-holelike with the Rashba spin-orbit coupling term depending on momentum both linearly and cubically while that in Ge/SiGe quantum wells is a heavy-hole state with the Rashba spin-orbit coupling term depending on momentum only cubically. The hole spin relaxation is investigated by means of the fully microscopic kinetic spin Bloch equation approach with all the relevant scatterings considered. It is found that the hole-phonon scattering is very weak, which makes the hole-hole Coulomb scattering become very important. The hole system in Si/SiGe quantum wells is generally in the strong scattering limit while that in Ge/SiGe quantum wells can be in either the strong or the weak scattering limit. The Coulomb scattering leads to a peak in both the temperature- and hole-density dependences of spin relaxation time in Si/SiGe quantum wells, located around the crossover between the degenerate and nondegenerate regimes. Nevertheless, the Coulomb scattering leads to not only a peak but also a valley in the temperature dependence of spin relaxation time in Ge/SiGe quantum wells. The valley is actually due to the crossover from the weak to strong scattering limit. The hole-impurity scattering influences the spin relaxation effectively. In the strong (weak) scattering limit, the spin relaxation time increases (decreases) with increasing impurity density. The spin relaxation time is found to be on the order of $1\ensuremath{\sim}100\text{ }\text{ps}$ $(0.1\ensuremath{\sim}10\text{ }\text{ps})$ in Si/SiGe (Ge/SiGe) quantum wells, for the temperatures, carrier/impurity densities and gate voltages of our consideration.