三角形截面GaN纳米线中的Frohlich电子-声子相互作用哈密顿

Frohlich electron-phonon interaction Hamiltonian in GaN nanowires with triangular cross-section

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Frohlich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。

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 Frohlich¨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.