Comparison of the $k⋅p$ and direct diagonalization approaches to the electronic structure of InAs/GaAs quantum dots

We present a comparison of the 8-band $k⋅p$ and empirical pseudopotential approaches to describing the electronic structure of pyramidal InAs/GaAs self-assembled quantum dots. We find a generally good agreement between the two methods. The most significant differences found in the $k⋅p$ calculation are (i) a reduced splitting of the electron p states (3 vs 24 meV), (ii) an incorrect in-plane polarization ratio for electron-hole dipole transitions (0.97 vs 1.24), and (iii) an over confinement of both electron (48 meV) and hole states (52 meV), resulting in a band gap error of 100 meV. We introduce a “linear combination of bulk bands” technique which produces results similar to a full direct diagonalization pseudopotential calculation, at a cost similar to the $k⋅p$ method.