  In order to study heterostructures composed both of materials with strongly
different parameters and of materials with narrow band gaps, we have developed
an approach, which combines the spherical 8-band effective-mass Hamiltonian and
the Burt's envelope function representation. Using this method, electron and
hole states are calculated in CdS/HgS/CdS/H_2O and CdTe/HgTe/CdTe/H_2O
quantum-dot quantum-well heterostructures. Radial components of the wave
functions of the lowest S and P electron and hole states in typical quantum-dot
quantum wells (QDQWs) are presented as a function of radius. The 6-band-hole
components of the radial wave functions of an electron in the 8-band model have
amplitudes comparable with the amplitude of the corresponding 2-band-electron
component. This is a consequence of the coupling between the conduction and
valence bands, which gives a strong nonparabolicity of the conduction band. At
the same time, the 2-band-electron component of the radial wave functions of a
hole in the 8-band model is small compared with the amplitudes of the
corresponding 6-band-hole components. It is shown that in the CdS/HgS/CdS/H_2O
QDQW holes in the lowest states are strongly localized in the well region
(HgS). On the contrary, electrons in this QDQW and both electron and holes in
the CdTe/HgTe/CdTe/H_2O QDQW are distributed through the entire dot. The
importance of the developed theory for QDQWs is proven by the fact that in
contrast to our rigorous 8-band model, there appear spurious states within the
commonly used symmetrized 8-band model.
