%X Lead dioxide has been used for over a century in the lead-acid battery. Many fundamental questions concerning PbO2 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 PbO2, using a hybrid density functional, and show that it is an n-type semiconductor with a small indirect band gap of ∼0.2  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. %C US %O © 2011 American Physical Society %L discovery1395992 %J Physical Review Letters %D 2011 %A DO Scanlon %A AB Kehoe %A GW Watson %A MO Jones %A WI David %A DJ Payne %A RG Egdell %A PP Edwards %A A Walsh %V 107 %T Nature of the band gap and origin of the conductivity of PbO2 revealed by theory and experiment. %N 24