Analytical obtention of eigen-energies for lens-shaped quantum dot with finite barriers

Details Analytical obtention of eigen-energies for lens-shaped quantum dot with finite barriers Analytical obtention of eigen-energies for lens-shaped quantum dot with finite barriers

2008-10-08

arxiv.org/abs/0810.1454v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, 3 figures, accepted for publication in The European Physical Journal B

Scientific paper

10.1140/epjb/e2008-00394-3

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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