Effect of band anisotropy on electronic structure of PbS, PbSe, and PbTe quantum dots

We have calculated the electronic structure of spherical PbS, PbSe, and PbTe quantum dots using a four-band envelope-function formalism that accounts for band anisotropy. By comparing our results with an analytical calculation that assumes a spherical approximation of the $\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{p}$ Hamiltonian, we show that the effects of band anisotropy are more pronounced for the excited states and increase with the confinement. We also show how the same technique can be applied to ellipsoidal quantum dots.