Comparison of the $k⋅p$ and the direct diagonalization approaches for describing the electronic structure of quantum dots

It is shown that the standard (decoupled) $6×6 k⋅p$ effective-mass approach for semiconductor quantum dots overestimates significantly the hole and electron confinement energies, and, for dots made of materials with small spin-orbit coupling (e.g., phosphides, sulphides) produces a reverse order of s- and p-like valence states. By contrasting the electronic structures of dots as obtained by a direct diagonalization (multiband) pseudopotential approach and by its $k⋅p$ approximation, we are able to trace the systematic errors of $k⋅p$ in dots to the $k⋅p$ errors in the underlying bulk solids. This suggests a “diagnostic tool” and a strategy for improving the $k⋅p.$