柱形量子线中的电—声子相互作用
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摘要
随着分子束外延等超薄生长技术和精细束加工技术的不断发展和完善,使人们能够按照自己的意愿排列原子、分子,制备出各种各样的零维、一维和二维纳米结构,甚至单分子器件.由于这些低维纳米体系不仅具有极其丰富的物理内涵和独特的性能,而且具有极其广阔的应用前景,因而对它们的研究在当代物理学、材料学以及日新月异的高新技术领域中显得极为重要.本文采用变分法和类LLP变换,并利用有效质量近似原理,系统地研究了柱形量子线中的杂质态和激子态的性质.分别在无限深势阱和有限深势阱中讨论了,电子与约束体纵光学(LO)声子、界面光学声子(IO)相互作用影响下的杂质态的行为.详细地讨论了电子极化效应以及杂质离子-声子相互作用对杂质态结合能的贡献行为.并进一步考虑了外加电场对量子线中杂质态、激子态极化效应的影响.获得的结果主要有:
一、利用变分法和有效质量近似原理,计算了LO声子场和IO声子场对杂质态结合能的影响.计算中采用约束型电.声子相互作用哈密顿量,不仅考虑了电子与约束LO、IO声子的相互作用,而且还计入了杂质离子与约束LO、IO声子模的相互作用,并以外层包裹着一层非极性材料的GaAs柱形量子线为例进行数值计算.结果表明,只考虑电子和声子耦合的杂质态结合能较不考虑任何声子影响的杂质态结合能略有提高;但是计入了杂质离子和声子的耦合后,结合能大大降低,即考虑了声子场的极化效应使杂质态结合能较不考虑声子场影响有所降低.还给出了杂质态结合能随杂质位置的变化关系,发现当杂质偏离阱中心时,结合能及LO声子对结合能的影响将降低.此外,对电子的有效质量修正也作了讨论.
二、考虑在垂直于量子线轴的方向上加外电场的情形,运用变分法计算了外电场作用下杂质态的极化效应.结果表明杂质态结合能不只是量子线半径的函数,它还随杂质位置,外电场强度发生变化.发现外加电场降低了杂质态结合能,考虑声子场作用后杂质态的斯塔克能移有所减小.另外,当杂质位置偏离阱中心时,系统对称性被破坏,外电场施加的方向也将影响杂质态结合能的大小.同时还对比了CdTe(Ⅱ-Ⅵ)及GaAs(Ⅲ-Ⅴ)两种材料中杂质态结合能的情况,发现CdTe材料中的杂质态结合能较GaAs材料中的高,且前者的极化效应及量子约束斯塔克效应较后者更明显.
三、将模型进一步改进,考虑有限深柱形量子线中类氢杂质态的性质.采用约束型电-声子相互作用哈密顿量计算了杂质态的极化效应,不仅考虑了电子与LO声子、IO声子的相互作用,同时还计入了杂质离子与各约束型声子模的相互作用.以GaAs材料为例进行数值计算,结果表明,有限深柱形量子线中杂质离子-声子耦合降低了杂质态结合能,并且对结合能移动有重要贡献;而电子的极化效应提高了杂质态结合能,但对结合能影响不是很大.在杂质势屏蔽效应中,LO声子模对结合能的贡献要大于IO声子的贡献.对于电子极化效应来说,在量子线半径比较小的时候,IO声子模对结合能的影响起主要作用;而在量子线半径增大时,LO声子模的贡献变得更重要.
四、利用变分方法计算了外电场影响下有限深GaAs柱形量子线中杂质态的极化效应.给出了杂质态结合能在不同的电场强度下随量子线半径、杂质位置的变化关系.结果表明,考虑声子场作用后杂质态的结合能和斯塔克能移有所减小.在外电场的影响下结合能的峰值向半径大的方向移动.
五、研究了外电场作用下,激子-声子相互作用对无限深柱形量子线中的激子结合能的影响.以Ⅲ-Ⅴ和Ⅱ-Ⅵ化合物半导体量子线为例,给出了激子结合能随量子线半径和电场的变化关系.结果表明,激子-声子相互作用减小了激子的结合能和斯塔克能移,计算激子结合能时声子极化场的影响不能忽略.
With the development of molecular-beam epitaxy and microfabrication techniques, people can arrange the atoms and moleculars at will and make various zero-dimensional, one-dimensional and two-dimensional systems even single molecular devices. Those low-dimensional systems not only have unique physical properties, but also extra wide application prospects. Therefore, it is important to study those systems in the modern physics, the material physics and the developing technique. In this paper, variational method and Lee-Low-Pines (LLP)-like transformations are applied to investigate the impurity states and exciton states in effective mass approximation in a cylindrical quantum wire. The properties of the impurity states with the influences of the electron- confined longitudinal optical (LO) phonon and interface optical (10) phonon interactions in the infinite and finite quantum wires are studied. In addition, the contributions of the electron polaronic effects and impurity center-phonon couplings to the impurity binding energies are discussed in detail. Finally, the phonon effects on the impurity and exciton binding energies under an external electric field are investigated. Some main results obtained in the thesis are generalized as following:
[1] Variational method and effective mass approximation are applied to calculate the phonon effects on the impurity binding energy in a GaAs cylindrical quantum wire surrounded by a nonpolar material. For the electron-phonon interaction we use the electron-confined LO and IO phonon interaction Hamiltonian and take both the electron- phonon couplings as well as the impurity-ion phonon couplings into account. The results show that the binding energies with only the electron polaronic effects are slightly higher than that without any phonon influence. Once taking ion-phonon couplings into account, the binding energies are obviously lower than that without phonon contributions. The impurity binding energies for different impurity position in the quantum wire are also calculated and find that the binding energies and the LO phonon effects on the binding energies decrease rapidly as the impurity shifts away from the center. Besides, the renormalization effective mass of the electron bound to the impurity center in quantum wire center is also concluded.
[2] Variational approach is applied to calculate the binding energy of bound impurity states in a cylindrical quantum wire under an external electric field perpendicular to the quantum wire axes. The results show that the binding energies of shallow donor impurity states strongly depend not only on the wire radius, but also on the applied electric field and the impurity position in the wire. The binding energy is reduced by the external electric field and the phonon effects. The effect of the electric field direction becomes significant when the impurity departs from the wire center. Compared with the GaAs (III-V) quantum wire, the impurity binding energy is higher in the CdTe (II-VI) quantum wire, and the phonon effects and Stark shifts are larger in the CdTe quantum wire.
[3] The binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well are discussed. The phonon effects on the impurity states are considered by taking both the couplings of the electron- confined LO and IO phonon and the impurity ion-LO and IO phonon into account. As an example, we have performed numerical calculation in a GaAs cylindrical quantum wire. It is found that the ion-phonon interactions reduce the impurity binding energy and supply a key contribution to the energy shifts, but the electron polaronic effects enhance the binding energy less. LO phonon effect plays more important role than IO phonon in the impurity potential screening. The electron polaronic effect caused by IO phonon is more important when the wire is thinner, while the LO phonon effect is dominant for the thicker wires.
[4] The effects of the external electric field on the hydrogenic impurity states in the GaAs quantum wire with a finite confining potential are studied by a variational method. The binding energies are calculated as functions of the transverse dimension of the quantum wire, and the donor-impurity position for different electric fields. The calculated results confirm that the phonon effects both reduce the binding energies of impurity states and the Stark shifts. The peak of the binding energies shifts toward a larger radius when the external electric field is applied.
[5] The effects of the exciton- phonon interactions on the binding energies of an exciton in a cylindrical quantum wires with infinite potential in present an external electric filed are discussed. The exciton binding energies for III-V and II-VI compound semiconductor quantum wire structure are calculated as functions of the transverse dimension of the quantum wires and the electric fields. Theoretical results show that the exciton-phonon coupling reduces both the exciton binding energies and the Stark shifts by screening the Coulomb interaction and cannot be neglected.
一、利用变分法和有效质量近似原理,计算了LO声子场和IO声子场对杂质态结合能的影响.计算中采用约束型电.声子相互作用哈密顿量,不仅考虑了电子与约束LO、IO声子的相互作用,而且还计入了杂质离子与约束LO、IO声子模的相互作用,并以外层包裹着一层非极性材料的GaAs柱形量子线为例进行数值计算.结果表明,只考虑电子和声子耦合的杂质态结合能较不考虑任何声子影响的杂质态结合能略有提高;但是计入了杂质离子和声子的耦合后,结合能大大降低,即考虑了声子场的极化效应使杂质态结合能较不考虑声子场影响有所降低.还给出了杂质态结合能随杂质位置的变化关系,发现当杂质偏离阱中心时,结合能及LO声子对结合能的影响将降低.此外,对电子的有效质量修正也作了讨论.
二、考虑在垂直于量子线轴的方向上加外电场的情形,运用变分法计算了外电场作用下杂质态的极化效应.结果表明杂质态结合能不只是量子线半径的函数,它还随杂质位置,外电场强度发生变化.发现外加电场降低了杂质态结合能,考虑声子场作用后杂质态的斯塔克能移有所减小.另外,当杂质位置偏离阱中心时,系统对称性被破坏,外电场施加的方向也将影响杂质态结合能的大小.同时还对比了CdTe(Ⅱ-Ⅵ)及GaAs(Ⅲ-Ⅴ)两种材料中杂质态结合能的情况,发现CdTe材料中的杂质态结合能较GaAs材料中的高,且前者的极化效应及量子约束斯塔克效应较后者更明显.
三、将模型进一步改进,考虑有限深柱形量子线中类氢杂质态的性质.采用约束型电-声子相互作用哈密顿量计算了杂质态的极化效应,不仅考虑了电子与LO声子、IO声子的相互作用,同时还计入了杂质离子与各约束型声子模的相互作用.以GaAs材料为例进行数值计算,结果表明,有限深柱形量子线中杂质离子-声子耦合降低了杂质态结合能,并且对结合能移动有重要贡献;而电子的极化效应提高了杂质态结合能,但对结合能影响不是很大.在杂质势屏蔽效应中,LO声子模对结合能的贡献要大于IO声子的贡献.对于电子极化效应来说,在量子线半径比较小的时候,IO声子模对结合能的影响起主要作用;而在量子线半径增大时,LO声子模的贡献变得更重要.
四、利用变分方法计算了外电场影响下有限深GaAs柱形量子线中杂质态的极化效应.给出了杂质态结合能在不同的电场强度下随量子线半径、杂质位置的变化关系.结果表明,考虑声子场作用后杂质态的结合能和斯塔克能移有所减小.在外电场的影响下结合能的峰值向半径大的方向移动.
五、研究了外电场作用下,激子-声子相互作用对无限深柱形量子线中的激子结合能的影响.以Ⅲ-Ⅴ和Ⅱ-Ⅵ化合物半导体量子线为例,给出了激子结合能随量子线半径和电场的变化关系.结果表明,激子-声子相互作用减小了激子的结合能和斯塔克能移,计算激子结合能时声子极化场的影响不能忽略.
With the development of molecular-beam epitaxy and microfabrication techniques, people can arrange the atoms and moleculars at will and make various zero-dimensional, one-dimensional and two-dimensional systems even single molecular devices. Those low-dimensional systems not only have unique physical properties, but also extra wide application prospects. Therefore, it is important to study those systems in the modern physics, the material physics and the developing technique. In this paper, variational method and Lee-Low-Pines (LLP)-like transformations are applied to investigate the impurity states and exciton states in effective mass approximation in a cylindrical quantum wire. The properties of the impurity states with the influences of the electron- confined longitudinal optical (LO) phonon and interface optical (10) phonon interactions in the infinite and finite quantum wires are studied. In addition, the contributions of the electron polaronic effects and impurity center-phonon couplings to the impurity binding energies are discussed in detail. Finally, the phonon effects on the impurity and exciton binding energies under an external electric field are investigated. Some main results obtained in the thesis are generalized as following:
[1] Variational method and effective mass approximation are applied to calculate the phonon effects on the impurity binding energy in a GaAs cylindrical quantum wire surrounded by a nonpolar material. For the electron-phonon interaction we use the electron-confined LO and IO phonon interaction Hamiltonian and take both the electron- phonon couplings as well as the impurity-ion phonon couplings into account. The results show that the binding energies with only the electron polaronic effects are slightly higher than that without any phonon influence. Once taking ion-phonon couplings into account, the binding energies are obviously lower than that without phonon contributions. The impurity binding energies for different impurity position in the quantum wire are also calculated and find that the binding energies and the LO phonon effects on the binding energies decrease rapidly as the impurity shifts away from the center. Besides, the renormalization effective mass of the electron bound to the impurity center in quantum wire center is also concluded.
[2] Variational approach is applied to calculate the binding energy of bound impurity states in a cylindrical quantum wire under an external electric field perpendicular to the quantum wire axes. The results show that the binding energies of shallow donor impurity states strongly depend not only on the wire radius, but also on the applied electric field and the impurity position in the wire. The binding energy is reduced by the external electric field and the phonon effects. The effect of the electric field direction becomes significant when the impurity departs from the wire center. Compared with the GaAs (III-V) quantum wire, the impurity binding energy is higher in the CdTe (II-VI) quantum wire, and the phonon effects and Stark shifts are larger in the CdTe quantum wire.
[3] The binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well are discussed. The phonon effects on the impurity states are considered by taking both the couplings of the electron- confined LO and IO phonon and the impurity ion-LO and IO phonon into account. As an example, we have performed numerical calculation in a GaAs cylindrical quantum wire. It is found that the ion-phonon interactions reduce the impurity binding energy and supply a key contribution to the energy shifts, but the electron polaronic effects enhance the binding energy less. LO phonon effect plays more important role than IO phonon in the impurity potential screening. The electron polaronic effect caused by IO phonon is more important when the wire is thinner, while the LO phonon effect is dominant for the thicker wires.
[4] The effects of the external electric field on the hydrogenic impurity states in the GaAs quantum wire with a finite confining potential are studied by a variational method. The binding energies are calculated as functions of the transverse dimension of the quantum wire, and the donor-impurity position for different electric fields. The calculated results confirm that the phonon effects both reduce the binding energies of impurity states and the Stark shifts. The peak of the binding energies shifts toward a larger radius when the external electric field is applied.
[5] The effects of the exciton- phonon interactions on the binding energies of an exciton in a cylindrical quantum wires with infinite potential in present an external electric filed are discussed. The exciton binding energies for III-V and II-VI compound semiconductor quantum wire structure are calculated as functions of the transverse dimension of the quantum wires and the electric fields. Theoretical results show that the exciton-phonon coupling reduces both the exciton binding energies and the Stark shifts by screening the Coulomb interaction and cannot be neglected.
引文
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