有限势垒透镜状量子点本征能量的解析计算
Analytical obtention of eigen-energies for lens-shaped quantum dot with finite barriers
摘要：
在包络函数近似下，得到了有限限制势透镜状量子点中粒子的束缚态。量子点具有半径为$a$和最大帽高度为$b$的圆形基底，并且认为粒子的有效质量在点的内部和外部不同。一个二维傅立叶展开是用在一个半球域与无限的墙壁，其中包含的几何形状的原始潜力。计算了不同透镜变形$b/a$、透镜半径$a$和势垒高度$V_o$时的电子能量。在很高的限制势的限制下，无限势垒的情况下的结果恢复。
英文摘要：
The bound states of a particle in a lens-shaped quantum dot with finite confinement potential are obtained in the envelope function approximation. The quantum dot has circular base with radius $a$ and maximum cap height $b$, and the effective mass of the particle is considered different inside and outside the dot. A 2D Fourier expansion is used in a semi-sphere domain with infinite walls which contains the geometry of the original potential. Electron energies for different values of lens deformation $b/a$, lens radius $a$ and barrier height $V_o$ are calculated. In the very high confinement potential limit, the results for the infinite barrier case are recovered.
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