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

We report on a theoretical study of the hole states in II-IV quantum dots of spherical and ellipsoidal shapes, described by smooth potential confinement profiles that can be modeled by Gaussian functions in all three dimensions. The universal dependencies of the hole energy, g factor, and localization length on the quantum dot barrier height, as well as the ratio of effective masses of the light and heavy holes are presented for the spherical quantum dots. The splitting of the fourfold degenerate ground state into two doublets is derived for anisotropic (oblate or prolate) quantum dots. Variational calculations are combined with numerical ones in the framework of the Luttinger Hamiltonian. Constructed trial functions are optimized by comparison with the numerical results. The effective hole g factor is found to be independent of the quantum dot size and barrier height and is approximated by a simple universal expression depending only on the effective mass parameters. The results can be used for interpreting and analyzing experimental spectra measured in various structures with quantum dots of different semiconductor materials.