Group-V impurities in ${\text{SnO}}_2$ from first-principles calculations

By means of first-principles calculations we investigate the effects of N, P, As, and Sb impurities on the electrical properties of ${\text{SnO}}_2$. We find that N prefers to occupy the O site and unexpectedly acts as a very deep acceptor with a level closer to the conduction band than to the valence band. P, As, and Sb prefer the Sn site, where they act as shallow donors. The group-V impurities are therefore not suitable for achieving $p$-type conductivity in ${\text{SnO}}_2$, but P, As, and Sb may serve as $n$-type dopants. We also investigate the interaction between N and H impurities, finding that the binding energy of the N-H complex is much larger than the binding energies found for complexes involving H and group-IIIA impurities in ${\text{SnO}}_2$.

Figure 1

(Color online) (a) Calculated band structure for ${\text{SnO}}_2$ using the HSE hybrid functional. The VBM is set to zero on the energy axis. (b) Brillouin zone for rutile, indicating high-symmetry points included in the band-structure plot.

Figure 2

(Color online) Calculated formation energies for N substituting on the O site in ${\text{SnO}}_2$ using the HSE hybrid functional. N is found to be highly unstable when substituting on the Sn site. The bounds are shown for the formation energies corresponding to the extremes of O-poor and O-rich limits.

Figure 3

(Color online) Relaxed configurations of N substituting on the O site in ${\text{SnO}}_2$ using the HSE hybrid functional. The spin density isosurface, set to 10% of its maximum value, is also shown for the neutral ${\text{N}}_{\text{O}}$, displaying the highly localized hole state oriented in the 110 direction.

Figure 4

(Color online) Calculated formation energies for substitutional P-related defects in ${\text{SnO}}_2$ using the HSE hybrid functional. The bounds are shown for the formation energies corresponding to the extreme O-poor and O-rich limits.

Figure 5

(Color online) Calculated formation energies for substitutional As-related defects in ${\text{SnO}}_2$ using the HSE hybrid functional. The bounds are shown for the formation energies corresponding to the extreme O-poor and O-rich limits.

Figure 6

(Color online) Calculated formation energies for ${\text{Sb}}_{\text{Sn}}$ in ${\text{SnO}}_2$. The ${\text{Sb}}_{\text{Sn}}$ defect was found to be considerably higher in formation energy and therefore highly unlikely to form. Both O-rich and O-poor limiting conditions are shown.

Figure 7

(Color online) Calculated formation energies for substitutional N on the O site and its neutral complex with interstitial hydrogen. Bounds for the impurity and complex formation energies correspond to the extreme O-poor and O-rich limits.