Fig. 1. (Color online) Band gaps and band alignments between rutile SnO₂ and TiO₂. In (a) the band gaps of SnO₂ is taken from Ref. [15] and the CB band alignment is taken from Ref. [19], while in (b) both of them are calculated in this work. The band gap of TiO₂ is always set to its experimental value (taken from Ref. [20]).

Fig. 2. (Color online) (a) Primitive unit cells and (b) calculated total and partial density of states for rutile SnO₂ and TiO₂. The green, blue and purple balls represent Sn, Ti and O respectively. (c) Side view of the atomic configuration for SnO₂/TiO₂ heterojunction (top panel).

Fig. 3. (Color online) (a) Band structure of SnO₂ along two high symmetry lines M–Γ–Z. (b) Optical absorption coefficient of SnO₂. The valence band maximum is set at zero. In (a), the red and green arrows represent the possible optical transitions at Γ-point and away from Γ-point, respectively.

Fig. 4. (Color online) Differences between the HSE06 + G₀W₀ calculated and experimentally measured band gaps for a series of oxides.

Fig. 5. (Color online) Calculated DOS of SnO₂ for the valence bands below VBM level. The right-hand side shows the DOS with enlarged energy scale below the VBM at E = 0 eV.

Table 1. The calculated optical transition matrix elements (in arbitrary units) between the valence band states and conduction band states for rutile SnO₂. Three transition paths are considered: two are at Γ-point and one is at the vicinity of Γ-point, as shown in Fig. 3. The energy for the valance (E_VB) and conduction band states (E_CB) are calculated with respect to the VBM and their energy difference is ΔE = E_CB – E_VB.

Table 2. Calculated fundamental band gaps (eV) of rutile TiO₂ and SnO₂ using different calculation methods and functionals.

Table 3. The calculated fundamental band gaps by HSE06 + G₀W₀ method ( ), the experimental band gaps ( ), and their difference ( ) for ZnO, CdO, Ga₂O₃, In₂O₃, GeO₂ and SnO₂.