Polar Mixing Optical Phonon Spectra in Wurtzite GaN Cylindrical Quantum Dots: Quantum Size and Dielectric Effects

混合 quasi-zero-dimensional (QoD ) 的声子模式的 interface-optical-propagating (IO-PR ) wurtzite 圆柱的量点(QD ) 结构被雇用宏观的绝缘的连续统模特儿导出并且学习。混合模式的 IO-PR 的分析声子状态被给。有混合声子模式的 IO-PR 的二种类型，这被发现，即混合在 QoD wurtzite QD 存在的模式的 -IO/z-PR 混合模式和 z-IO/-PR。并且各， IO-PR 混合模式也有对称并且 antisymmetrical 表格。经由领域量子化的一个标准过程， Fr ? 电子的 hlich Hamiltonians --(IO-PR ) 混合声子相互作用被获得。wurtzite 上的数字计算轧了圆柱的 QD 被执行。结果表明光线方向的尺寸和轴方向的尺寸以及绝缘的矩阵在混合声子模式的 IO-PR 的散频率上有大影响。这些声子模式的散曲线的限制特征深入地被讨论。减少的声子模式“ wurtzite 量的行为限制了系统在结构显然被观察了。而且，在 wurtzite Q2D QW 和 Q1D QWR 系统在 wurtzite QoD QD 混合声子模式到 IO 模式和 PR 模式的 IO-PR 的堕落行为物理和数学的观点从两个深深地被分析。

The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric continuum model. The analytical phonon states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e. p-IO//z-PR mixing modes and the z-IO//p-PR mixing modes existing in QOD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrieal forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-（IO-PR） mixing phonons interaction are obtained. Numerical calculations on a wurtzite GaN cylindrical QD are performed. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes ＂reducing＂ behavior of wurtzite quantum confined systems has been observed obviously in the structures. Moreover, the degenerating behaviors of the IO-PR mixing phonon modes in wurtzite QOD QDs to the IO modes and PR modes in wurtzite Q2D QW and QID QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.