Anomalous splitting of the hole states in silicon quantum dots with shallow acceptors

Hole wavefunctions and energy spectra have been calculated in a silicon quantum dot with a shallow acceptor. Within the framework of the envelope function approach we have found anomalously strong splitting of the energy levels caused by the Coulomb and the spin-orbit interactions as compared to bulk silicon. If the quantum dot has been doped with boron, the short range part of the Coulomb field turns out to be weak, and the long range hydrogenic part plays a crucial role in the energy splitting. In the case where the dot is doped with any other element of the third group, the role of the short range Coulomb interaction becomes determinative. The latter provides stronger energy splitting compared to that in the model of hydrogen-like impurity. In both cases the energy of the splitting substantially exceeds the typical bulk values for these acceptors due to the quantum confinement effect. We have also analysed the charge distribution in the dot and the hole spectrum, depending on the acceptor position inside the nanocrystal.