Thermoabsorption in SnO2

Tin dioxide from first principles: Quasiparticle electronic states and optical properties

“…Our calculated band structure does not exhibit the conjectured lowerlying VBs approximately 0.2 or 0.4 eV below the VBM. 23,24 Although we observe that the next-lowest VB level is a doubly degenerate state with the Γ − 5 irreducible representation, which is consistent with the same set of experiments, 23,24 it occurs only at 0.71 eV below the VBM and thus cannot account for their observations.…”

“…The earliest self-consistent calculations for SnO 2 , employing the augmented-plane-wave 11 and linearized muffin-tin orbital 9 methods, along with more recent ones in the augmented-spherical-wave 12 method, predicted an indirect gap with the VBM at the R point instead of Γ. Tightbinding calculations by Robertson 8 seemed more consistent with the experimental interpretations of a direct gap and highestlying VB symmetry assignments, by showing a VB of the suggested symmetry Γ − 5 approximately 0.2 eV below the VBM. 15,[22][23][24] However, the next lower VB in Robertson's calculations was at −0.8 eV, which cannot explain the experimentally observed absorption onsets and interpretations. As expected, calculations within the local-density or generalized gradient approximation (LDA, GGA, respectively) lead to a very strong underestimation of the fundamental band gap.…”

“…13,14,21 Accordingly, the respective onsets in single-photon optical absorption experiments are weak. [21][22][23][24][25] Despite the relatively small absorption coefficients, these experiments have revealed the polarization dependence of the onsets. While the transitions are dipole-forbidden in single-photon absorption, they are allowed in two-photon absorption, and the measured value of 3.6 eV 10,26 is now widely accepted as the band gap of SnO 2 .…”

“…Nagasawa and Shionoya reported an allowed transition value of 3.75 eV for light polarized perpendicular to the tetragonal c axis (E ⊥ c), which they associated with a VB of symmetry Γ − 5 lying 0.15 to 0.20 eV below the VBM. 15 For light polarized parallel to c (E c), the absorption spectra exhibit a diffuse edge approximately 0.4 eV above the fundamental edge, [22][23][24] lacking the fine excitonic structure of the absorption spectra for perpendicular light polarization. 10,13,14,24 This feature was assigned to a hypothetical valence band with Γ − 2 symmetry 23,24 lying 0.4 eV eV below the Γ + 3 VBM, consistent with their interpretation of direct, symmetry-allowed transitions in the same study.…”

“…[22][23][24] Up until now no theoretical band structure is capable of explaining all experimental facts for SnO 2 . The earliest self-consistent calculations for SnO 2 , employing the augmented-plane-wave 11 and linearized muffin-tin orbital 9 methods, along with more recent ones in the augmented-spherical-wave 12 method, predicted an indirect gap with the VBM at the R point instead of Γ. Tightbinding calculations by Robertson 8 seemed more consistent with the experimental interpretations of a direct gap and highestlying VB symmetry assignments, by showing a VB of the suggested symmetry Γ − 5 approximately 0.2 eV below the VBM.…”