三角形截面GaN 纳米线中的Fr¨ohlich 电子-声子相互作用哈密顿

doi:10.3969/j.issn.1007-5461.2022.04.019

量子电子学报 ›› 2022, Vol. 39 ›› Issue (4): 632-643.doi: 10.3969/j.issn.1007-5461.2022.04.019

三角形截面GaN 纳米线中的Fr¨ohlich 电子-声子相互作用哈密顿

张立1∗, 王琦2

( 1 广州番禺职业技术学院智能制造学院, 广东番禺511483; 2 北京大学东莞光电研究院, 广东东莞523429 )

收稿日期:2021-07-12 修回日期:2021-08-27 出版日期:2022-07-28 发布日期:2022-07-28
通讯作者: E-mail: zhangli-gz@263.net E-mail:E-mail: zhangli-gz@263.net
作者简介:张立( 1976 - ), 湖北人, 博士, 教授, 主要从事低维量子系统中的电子态、杂质态、电子-声子相互作用以及非线性光学特性等理论方面的研究。E-mail: zhangli-gz@263.net
基金资助:
Supported by the Fundamental Research and Applied Fundamental Research Fund of Guangzhou City (2021 年广州市基础与应用基础研究计划项目)

Fr¨ohlich electron-phonon interaction Hamiltonian in GaN nanowires with triangular cross-section

Zhang Li1∗, Wang Qi2

(1 School of Intelligent Manufacturing, Guangzhou Panyu Polytechnic, Panyu 511483, China; 2 Dongguan Institute of Opto-Electronics, Peking University, Dongguan 523808, China)

Received:2021-07-12 Revised:2021-08-27 Published:2022-07-28 Online:2022-07-28

摘要/Abstract

摘要： 基于介电连续模型, 推导和分析了具有等边三角形截面的纤锌矿GaN 纳米线结构中的极化光学声子模。研究发现该纳米线结构中存在的精确受限(EC) 声子模频率为GaN 材料自由z- 方向上的纵光学声子特征频率 ωz,L, 由于受限情况不同, 这明显不同于GaN-基量子阱中的情况。进而采用非分离变量法, 求解了该纳米线结构中EC 声子模静电势的Laplace 方程, 得到了EC 声子模的精确解析的声子态, 并导出了系统中的极化本征矢量及其正交关系, 自由声子场及相应的Fr¨ohlich 电子-声子相互作用哈密顿。最后以GaN 为例开展了数值计算, 绘制了电子-声子耦合函数空间分析情况, 对电子-声子耦合函数的对称性、耦合强度等性质进行了讨论, 并获得了有意义的结果。

关键词: 光电子学, 电－声子相互作用, 极化光学声子, 氮化镓纳米线, 三角形截面

Abstract: Polar optical phonon modes in wurtzite GaN nanowires with equilateral triangular crosssection are deduced and analyzed by using the dielectric continuum model. It is found that the frequency of exactly confined (EC) modes in the GaN nanowire systems is the characteristic frequency (ωz,L) of longitudinal-optical phonons in free z-direction, which is obviously different from the case of EC modes in wurtzite GaN-based quantum wells due to their different confined dimensions. Then by using the method of nonseparable variables, the Laplace equation of the electrostatic potential of the nanowire structure is solved, the exact analytical phonon states of EC modes are obtained, and the polarization eigenvectors and their orthogonal relations, the free phonon field, as well as the corresponding Fr¨ohlich electron-phonon interaction Hamiltonian for the EC phonon modes are also derived. Finally, the numerical calculation on GaN nanowire is performed, the electron-phonon coupling functions are depicted and discussed, the symmetries and coupling strength of the coupling functions are analyzed in detail, and some meaningful conclusions are drawn.

Key words: optoelectronics, electron-phonon interaction, polar optical phonon, GaN nanowire, triangular cross-section

中图分类号:

O481.1

张立∗, 王琦. 三角形截面GaN 纳米线中的Fr¨ohlich 电子-声子相互作用哈密顿[J]. 量子电子学报, 2022, 39(4): 632-643.

Zhang Li∗, Wang Qi. Fr¨ohlich electron-phonon interaction Hamiltonian in GaN nanowires with triangular cross-section[J]. Chinese Journal of Quantum Electronics, 2022, 39(4): 632-643.

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三角形截面GaN 纳米线中的Fr¨ohlich 电子-声子相互作用哈密顿

Fr¨ohlich electron-phonon interaction Hamiltonian in GaN nanowires with triangular cross-section

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