摘要
本文利用介电连续模型系统地研究了极性二元晶体构成的球形异质结构——双层和三层球形核壳量子点中的光学振动模及电—声子相互作用,并利用变分法对双层结构中的束缚极化子进行了讨论.在此基础之上,在球形异质结构中引入极性三元混晶材料,利用改进的无规元素孤立位移模型和有效声子近似,研究了含三元混晶的双层和三层球形核壳量子点中的三元混晶效应.主要研究结果如下：
一、利用介电连续模型研究了非极性材料包覆的双层球形核壳量子点中的界面／表面(IO/SO)声子模,给出了声子模的色散关系和电子-IO/SO声子相互作用的哈密顿量,并对CdSe/ZnS核壳量子点进行了数值计算.结果表明,双层结构中存在三支频率不同的IO/SO声子模,其频率不仅取决于核壳结构材料的有关参数,而且依赖于外层非极性材料的介电常数εd.三支声子势的变化趋势各不相同,且随着壳层厚度的增加,IO/SO声子模在界面或表面附近的局域性显著增强.并且发现,当εd较小时,频率较高的两支类ZnS IO/SO模对电—声子相互作用的贡献起主要作用,当εd较大时,表面极化效应明显减弱,频率最高的类ZnS SO模转变为类ZnS IO模,对电—声子相互作用的贡献起主要作用.随着角量子数的增大,IO/SO声子模对电—声子相互作用的贡献逐渐减小.
二、利用介电连续模型研究了三层球形核壳量子点中的IO/SO声子模,给出了声子模的色散关系和电—声子相互作用的哈密顿量,并对CdSe/ZnS/CdSe核壳量子点进行了数值计算.结果表明,三层结构中存在五支IO/SO声子模,其中频率较高的两支模为类ZnS IO模,频率较低的三支模为类CdSe IO/SO模,且五支模的频率均依赖于外层非极性材料的介电常数εd.同时发现,五支声子势的变化趋势各不相同,当εd较小时,类ZnS IO模及类CdSe SO模对电—声子相互作用的贡献起主要作用,当εd较大时,类CdSe SO模转变为类CdSe IO模,表面极化效应明显减弱.
三、利用改进的无规元素孤立位移模型(MREI)和有效声子近似(EPMA),研究了含三元混晶的双层和三层球形核壳量子点中的三元混晶效应,并对GaAs/AlxGa1-xAs和GaAs/AlxGa1-xAs/GaAs核壳量子点进行了数值计算.结果表明,球形核壳量子点中存在特殊的混晶效应,具体表现在,在组分取不同值时,不仅类AlxGa1-xAs IO/SO声子模的频率变化范围明显不同,而且类GaAs IO声子模的频率在一定范围内也会受到组分的影响.同时发现,各支IO/SO声子模的静电势随混晶组分的不同呈现不同的分布形态,因此组分的变化对电—声子相互作用有重要影响.
四、利用介电连续模型研究了三层球形核壳量子点中的受限LO声子模,给出了电子—LO声子相互作用的哈密顿量,并对CdSe/ZnS/CdSe核壳量子点进行了数值计算.结果表明,局域在CdSe核中的LO1声子和局域在ZnS壳层中的L02声子对电—声子相互作用的贡献是主要的,且LO2声子的声子势强度强烈依赖于ZnS壳层的厚度,随着壳层厚度的增加,声子势强度逐渐降低,对电—声子相互作用的贡献也相应地逐渐减小.
五、利用本文导出的电—声子相互作用哈密顿量,采用有效质量近似和变分法研究了双层球形核壳量子点中的束缚极化子,讨论中同时考虑了电子—声子和杂质—声子的耦合作用,并对ZnS/CdSe核壳量子点进行了数值计算.结果表明,杂质态结合能和声子极化效应均明显依赖于核半径和阱宽,声子效应明显地降低了杂质态的结合能.随着核半径和阱宽的减小,杂质态结合能明显增大；同时发现,存在一个临界阱宽,当阱宽小于临界阱宽时,杂质态的结合能明显增加,而且声子的贡献也显著增大.
Using the dielectric continuum approach (DCA), we have systematically investigated the optical vibration modes and electron-phonon interaction in a polar spherical multilayer core-shell quantum dot (CSQD) hosted in a non-polar material. The bound polarons in a bilayer CSQD have also been studied with a variational approach. On top of these, we introduce the polar ternary mixed crystals (TMC) into the spherical multilayer heterostructures, and investigate the TMC effects by applying the modified random-element-isodisplacement model (MREI) and effective-phonon-mode approximation (EPMA). The main results obtained are as following:
1. We have studied the optical vibration modes in a spherical bilayer CSQD in the framework of DCA. The dispersion relation and the corresponding electron-phonon interaction Hamiltonians for interface optical (IO) or surface optical (SO) phonons are derived. Numerical calculations are performed for a spherical CdSe/ZnS CSQD, and the results show that there are three branches frequencies of IO/SO phonon in the system, and phonon frequencies depend on the host medium. As shell thickness increases, the potentials of the IO/SO phonon modes more localized at a certain interface or surface. It is also found that the ZnS-like IO/SO modes with higher frequencies, compared with CdSe-like IO mode, have a strong electron-phonon coupling when εd is smaller. However for the bigger εd, ZnS-like SO mode is transformed into ZnS-like10mode, that means the surface polaron effect is greatly reduced. As the same time, the IO/SO phonon contribution to the electron-phonon interaction is decrease with increasing the angular quantum number.
2. The IO/SO phonon modes in a spherical three-layer CSQD are investigated by employing the DCA. The dispersion relation and the corresponding electron-phonon interaction Hamiltonians for IO/SO phonons are derived. Numerical calculations are performed for a spherical CdSe/ZnS/CdSe CSQD, and the results reveal that there are five branches frequencies of IO/SO phonon. Among these, the two modes with higher frequencies are ZnS-like IO modes, and the others with lower frequencies are CdSe-like IO/SO modes. The phonon frequencies depend on the geometrical and host material. It is observed that the electron-phonon coupling related to ZnS-like IO modes and CdSe-like SO mode is more significant when εd is smaller. Similarly, the surface polaron effect is much weaken for the larger εd, and CdSe-like SO mode switch to the outer interface.
3. We have studied the effects of TMC in spherical multilayer CSQD consisting of TMC by using MREI and EPMA. The numerical computations are performed for the spherical s and GaAs/AlxGa1-xAs/GaAs system. The results show that the frequencies of IO/SO modes strongly depend on the components of TMC, and the frequencies of GaAs-like IO modes also vary with the components in a certain range. Our investigations also indicate that the effects of TMC result in different distributions of IO/SO phonon potentials. Thus, the effects of TMC should be taken into account in the electron-phonon coupling investigation.
4. The confined longitudinal-optical (LO) phonon modes in a spherical three-layer CSQD have been studied in detail, and the corresponding electron-phonon interaction Hamiltonian is obtained by using the DCA. Numerical calculations are performed for a spherical CdSe/ZnS/CdSe CSQD, and the results reveal that the confined LO1phonon modes in the core material and the confined LO2phonon modes in the shell material, compared with the confined LO3phonon modes, are dominated in the electron-phonon coupling. At the same time, the potentials strength of LO2phonon is strongly dependent on the shell thickness, and the potentials strength decreases with the increasing of the shell thickness.
5. With the electron-phonon interaction Hamiltonians derived above, we have studied the polaron effects of an impurity in a spherical bilayer CSQD within the effective mass approximation. A adiabatic variational method is used to calculate the binding energy of the bound polaron, and both the electron-and ion-phonon effects are considered. It is indicated that phonon effects reduced obviously the impurity binding energy and depend on the core radius and the shell well width. When the shell well width is smaller than a critical value, both the impurity binding energy and the phonon effects increase significantly.
引文
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