Figure 1

Conceptual illustration of breaking of the dipole-forbidden transition rule in SnO₂ surfaces and nanocrystals. (a) Band structure and the corresponding optical absorption spectra of bulk SnO₂ calculated using generalized gradient approximation. (b) Crystal structure (left), partial charge density mappings of valence-band maximum (VBM) (middle) and conduction-band minimum (CBM) (right) of the SnO₂ (101) surface. (c) Band structure and the corresponding optical absorption spectrum of the SnO₂ (101) surface. (d) Partial charge densities of lowest unoccupied molecular orbital (left) and highest occupied molecular orbital (right) of a quantum dot (QD) with diameter of 1.5 nm. (e) Energy levels and the corresponding optical absorption spectrum of SnO₂ QD. For the ideal bulk SnO₂ with infinite dimensions, the absence of optical transition between VBM and CBM (corresponding to the fundamental bandgap) indicates that the band-edge light emission is dipole forbidden as a result of the symmetry of the band-edge wavefunctions. For the (101) surface and the QD with defects, the fundamental bandgap becomes dipole transition allowed, so the optical gap is largely reduced. As a consequence, the dipole-forbidden transition rule breaks down in SnO₂ surfaces and QDs.