Electron and hole states in quantum dot quantum wells within a spherical eight-band model

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 [E. P. Pokatilov et al., Phys. Rev. B 64, 245328 (2001), preceding paper)], which combines the spherical eight-band effective-mass Hamiltonian and the Burt's envelope-function representation. Using this method, electron and hole states are calculated in $\mathrm{CdS}/\mathrm{HgS}/\mathrm{CdS}/{\mathrm{H}}_{2}\mathrm{O}$ and $\mathrm{CdTe}/\mathrm{HgTe}/\mathrm{CdTe}/{\mathrm{H}}_{2}\mathrm{O}$ 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 (QDQW's) are presented as a function of radius. The six-band-hole components of the radial wave functions of an electron in the eight-band model have amplitudes comparable with the amplitude of the corresponding two-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 two-band-electron component of the radial wave functions of a hole in the eight-band model is small compared with the amplitudes of the corresponding six-band-hole components. It is shown that in the $\mathrm{CdS}/\mathrm{HgS}/\mathrm{CdS}/{\mathrm{H}}_{2}\mathrm{O} \mathrm{QDQW}$ 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 $\mathrm{CdTe}/\mathrm{HgTe}/\mathrm{CdTe}/{\mathrm{H}}_{2}\mathrm{O} \mathrm{QDQW}$ are distributed through the entire dot. The importance of the developed theory for QDQW's is proven by the fact that in contrast to our rigorous eight-band model, there appear spurious states within the commonly used symmetrized eight-band model.