We predict, by means of ab initio calculations, stable electron and hole polaron states in perfect monoclinic HfO 2 . Hole polarons are localized on oxygen atoms in the two oxygen sublattices. An electron polaron is localized on hafnium atoms. Small barriers for polaron hopping suggest relatively high mobility of trapped charges. The one-electron energy levels in the gap, optical transition energies and ESR g-tensor components are calculated. DOI: 10.1103/PhysRevLett.99.155504 PACS numbers: 61.72.Bb, 61.72.Ji, 71.15.Mb, 71.20.ÿb Control over carrier mobility in semiconductors and insulators under charge injection, photogeneration, or doping conditions is of enormous practical importance. In particular, the possibility of small electron and hole polaron formation in perfect deformable lattice (otherwise called self-trapping) has been considered in many studies (see for recent reviews). However, proving polaron self-trapping remains extremely challenging. Essentially, the subject of debate is whether the carrier trapping takes place at preexisting precursor states (shallow donor, acceptor, or defect states, disorder fluctuations) or whether the injected carriers self-trap in a perfect lattice, where the potential well is only created by the carrierinduced lattice polarization.Experimentally, distinguishing between trapping at defect sites and self-trapping in the perfect lattice is difficult due to crystal imperfection and generally small values of polaron self-trapping and migration energies. Reliable theoretical predictions, on the other hand, are rare, due to extreme sensitivity of the interplay between potential and kinetic energy of a polaron to a chosen Hamiltonian and boundary conditions (see, for example, Refs. [5,6]). The spectroscopic properties and diffusion barrier have been calculated for a number of systems, such as the selftrapped hole in alkali halides (V k center) [2,4], electron polaron in TiO 2 [7], and for a number of predominantly hole small polarons trapped at impurities (see, for example, Ref.[8]) and in amorphous silica [9].In this Letter we predict the self-trapping of both electrons and holes in the perfect monoclinic hafnium oxide (m-HfO 2 ) using static approach and density functional theory. HfO 2 has been in the spotlight of both scientists and engineers over the last ten years as a potential substitute for SiO 2 as a gate oxide in metal-oxidesemiconductor field-effect transistors (MOSFETs) [10]. The electron trapping in the dielectric layer in these devices may lead to degradation of their performance and reliability. The properties of the bulk HfO 2 are very similar to those of ZrO 2 , which has much wider abundance and range of applications. The primitive unit cell of m-HfO 2 (space group P2 1 =c) contains 12 atoms and two anion sublattices: in one oxygen ions are threefold coordinated (3C) and in the other -fourfold coordinated (4C).Recent theoretical calculations predicted polaronlike electron trapping near neutral oxygen vacancies in m-HfO 2 [11][12][13] and in the hypothet...