Role of semi core levels in determining the band-gaps of semiconductors: First-principles calculations with model Hamiltonians

First principle calculations based on LDA/GGA approximation for the exchange functional underestimate the position of the semi core 3d levels in GaX (X = N, P and As) semiconductors. A self-interaction correction scheme within the LDA+U/GGA+U approximation is found to be sufficient to correct this discrepancy. A consequence of thiscorrection is that the bandgap (E_g) of the semiconductors also improves. The belief has been that the bandgap correction comes from modified semi core-valence interaction. We examine this often used approximation in great detail and find that although bandgap changes as large as 0.63 eV for GaAs, 0.42 eV for GaP and 0.46 eV for GaN are obtained within this approach for U= 20 eV on the Ga d states, only 0.1 eV, 0.1 eV and 0.15 eV for GaAs, GaP and GaN arise from semi core-valence interaction. As U is increased, the bandgap keeps improving. We trace this effect primarily to the interaction of the Ga 4d states in the conduction band with the anion p states.