Quantum Confinement Effects and Electronic Properties of SnO 2 Quantum Wires and Dots

On the basis of the density functional theory (DFT) within local density approximations (LDA) approach, we calculate the band gaps for different size SnO 2 quantum wires (QWs) and quantum dots (QDs). A model is proposed to passivate the surface atoms of SnO 2 QWs and QDs. We find that the band gap increases between QWs and bulk evolve as Δ E g wire = 1.74/ d 1.20 as the effective diameter d decreases, while being Δ E g dot = 2.84/ d 1.26 for the QDs. Though the ∼ d 1.2 scale is significantly different from ∼ d 2 of the effective mass result, the ratio of band gap increases between SnO 2 QWs and QDs is 0.609, very close to the effective mass prediction. We also confirm, although the LDA calculations underestimate the band gap, that they give the trend of band gap shift as much as that obtained by the hybrid functional (PBE0) with a rational mixing of 25% Fock exchange and 75% of the conventional Perdew−Burke−Ernzerhof (PBE) exchange functional for the SnO 2 QWs and QDs. The relative deviation of the LDA calculated band gap difference Δ E g compared with the corresponding PBE0 result is only within 5%. Additionally, it is found the states of valence band maximum (VBM) and conduction band minimum (CBM) of SnO 2 QWs or QDs have a mostly p - and s -like envelope function symmetry, respectively, from both LDA and PBE0 calculations.