Energy levels of one and two holes in parabolic quantum dots

Calculations of energy levels of single-hole and two-hole states in a GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As parabolic quantum dot have been performed with a multiband effective-mass method. Both the valence-band degeneracy and the Coulomb interaction are taken into account using the axial approximation for the bulk band structure. The variational problem is solved with an iterative relaxation technique which allows us to use a large number of basis functions. The valence-band mixing is shown to be substantial and the Coulomb interaction between the holes leads to a resonant tunneling energy that is (in general) nonlinear with respect to the strength of the confinement potential. It is found that at sufficiently large confinement potentials, both the single-hole and two-hole ground states are changed from primarily heavy-hole-like to light-hole-like. © 1996 The American Physical Society.