Hydrogen interactions with acceptor impurities in ${\text{SnO}}_2$: First-principles calculations

Using first-principles calculations, we investigate the role of hydrogen in the passivation of Al, Ga, and In acceptors in ${\text{SnO}}_2$. We find that interstitial hydrogen bonds to oxygen atoms next to the acceptor impurities and effectively neutralizes their electrical activities. Based on calculated binding energies and migration barriers we discuss conditions under which hydrogen can be removed and acceptor activation can take place. We also calculate the stretch-mode vibrational frequencies associated with the hydrogen-impurity complexes, providing a signature for their experimental identifications.

Figure 1

(Color online) Calculated formation energies as a function of Fermi level for group III-A acceptors, interstitial hydrogen, and hydrogen-acceptor complexes in ${\text{SnO}}_2$. Results are shown for (a) Sn-rich and (b) O-rich conditions. The Fermi level varies from 0 at the VBM to 3.6 eV, which corresponds to the experimental band gap of ${\text{SnO}}_2$.

Figure 2

(Color online) Atomic configuration of an acceptor-hydrogen complex in ${\text{SnO}}_2$ showing the hydrogen atom and a substitutional ${\text{Ga}}_{\text{Sn}}$. The relaxed configuration is similar to that of the isolated ${\text{H}}_{\text{i}}^{+}$ but the primary ${\text{O}}_{\text{I}}\text{-H}$ bond length is slightly contracted while the distance to the secondary O neighbor ${\text{O}}_{\text{II}}\text{-H}$ is increased.

Figure 3

(Color online) Calculated potential-energy curve for an ${\text{O-H}}_{\text{i}}$ oscillator due to interstitial ${\text{H}}_{\text{i}}^{+}$ in ${\text{SnO}}_2$ (see inset). Large anharmonicity is evident. The curve is a fourth-order polynomial fit to the calculated data points. Calculated energy levels for the ground state and first excited state are shown, with schematics of the corresponding wave functions.