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

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 Vo are calculated. In the very high confinement potential limit, the results for the infinite barrier case are recovered