Abstract

The problem of exciton states in spherical semiconductor quantum dots is revisited, employing the finite element method to numerically solve the system of differential equations for the center of mass and relative motion of the interacting electron-hole pair. This process is performed within the effective mass and parabolic bands approximations. The use of a finite confinement together with a parabolic description of the conduction and valence band profiles prevents the two equations from uncoupling. The allowed energies are reported as functions of the quantum dot radius. A comparison of theoretically determined fundamental photoluminescence peak energies with available experimental reports in the cases of CdS, CdSe and CdTe is presented and discussed, showing a good agreement between calculated and measured results.

Graphical abstract

中文翻译：

---

球形量子点中的激子再探：胶体纳米晶体的分析

摘要

球形半导体量子点中的激子态问题，通过有限元方法，以数值方式求解了相互作用的电子-空穴对的质心和相对运动的微分方程组。在有效质量和抛物线近似范围内执行此过程。使用有限的限制以及对导带和价带分布的抛物线形描述可以防止两个方程解耦。所报告的能量是量子点半径的函数。给出并讨论了在CdS，CdSe和CdTe情况下理论上确定的基本光致发光峰值能量与可用的实验报告的比较，表明计算结果与测量结果之间有很好的一致性。

图形概要