The strong correlation of the 4f electrons of erbium in silicon

The local spin density approximation (LSDA) with the Hubbard model correction is adopted to describe the electronic structures of O-codoped Er-Si systems. The electrons in the 4f orbitals of Er atoms are taken as localized electrons in the framework of an all-electron treatment. The total density of states (DOS) and the partial densities of states for Si(3s, 3p), Er(4f), Er(5d), Er(6s), O(2s), and O(2p) in this ErSiO system are calculated. It is found that the inclusion of the Hubbard U greatly influences the partial DOS of the Er 4f electrons. The separation between the spin-up and the spin-down states of the highly localized 4f orbitals is larger than that of the LSDA results obtained without considering the Hubbard U-parameter. The calculation results provide possible explanations of the experimentally observed erbium-induced impurity energy levels in Si detected by deep-level transient spectroscopy.