Ground state of the holes localized in II-VI quantum dots with Gaussian potential profiles

摘要

We report on the theoretical study of the hole states in II-IV quantum dotsof a spherical and ellipsoidal shape, described by a smooth potentialconfinement profiles, that can be modelled by a Gaussian functions in all threedimensions. The universal dependencies of the hole energy, $g$-factor andlocalization length on a quantum dot barrier height, as well as the ratio ofeffective masses of the light and heavy holes are presented for the sphericalquantum dots. The splitting of the four-fold degenerate ground state into twodoublets is derived for anisotropic (oblate or prolate) quantum dots.Variational calculations are combined with numerical ones in the framework ofthe Luttinger Hamiltonian. Constructed trial functions are optimized bycomparison with the numerical results. The effective hole $g$-factor is foundto be independent on the quantum dot size and barrier height and isapproximated by simple universal expression depending only on the effectivemass parameters. The results can be used for interpreting and analyzingexperimental spectra measured in various structures with the quantum dots ofdifferent semiconductor materials.