Nature of the Band Gap and Origin of the Conductivity of ${\mathrm{PbO}}_2$ Revealed by Theory and Experiment

Lead dioxide has been used for over a century in the lead-acid battery. Many fundamental questions concerning ${\mathrm{PbO}}_2$ remain unanswered, principally: (i) is the bulk material a metal or a semiconductor, and (ii) what is the source of the high levels of conductivity? We calculate the electronic structure and defect physics of ${\mathrm{PbO}}_2$, using a hybrid density functional, and show that it is an $n$-type semiconductor with a small indirect band gap of $\sim 0.2\mathrm{eV}$. The origin of electron carriers in the undoped material is found to be oxygen vacancies, which forms a donor state resonant in the conduction band. A dipole-forbidden band gap combined with a large carrier induced Moss-Burstein shift results in a large effective optical band gap. The model is supported by neutron diffraction, which reveals that the oxygen sublattice is only 98.4% occupied, thus confirming oxygen substoichiometry as the electron source.

Figure 1

HSE06 calculated (a) electronic density of states for ${\mathrm{PbO}}_2$ with a gaussian smearing of 0.2 eV, (b) band structure for ${\mathrm{PbO}}_2$, with the position of the calculated charge neutrality level indicated by the horizontal dashed (green) line, and (c) theoretical optical absorption onset of ${\mathrm{PbO}}_2$.

Figure 2

Formation energies for intrinsic defects under O-rich conditions (left panel) and O-poor conditions (right panel).