Polaron-enhanced giant strain effect on defect formation: The case of oxygen vacancies in rutile TiO2

Recently, a semiconductor-to-metal transition was surprisingly observed in rutile ${\mathrm{TiO}}_{2}$ by applying just 5% tensile strain. To explore the mechanism behind this giant strain effect, we performed first-principles calculations focusing on the commonly existing oxygen vacancies (OVs) in rutile ${\mathrm{TiO}}_{2}$. We find that 5% biaxial tensile strain largely reduces the formation energies of OVs and biaxial compressive strain increases the formation energies of OVs. While our findings are in agreement with experiments, the giant strain effects on OV defect formation energies cannot be well explained by, or may even contradict, the common continuum elastic model. Our further studies show that strain not only induces elastic energy gain during defect formation, but also changes the polaronic configurations, which can have either energy gain or loss depending on the occupations of the excess electrons. The large reduction of OV formation energy under tensile strain is thus a combined effect of both elastic and polaronic energy gain. This giant strain effect, enhanced by polaronic effects on defect formation, might provide an alternative method for the manipulation of defects and electric conductivity in rutile ${\mathrm{TiO}}_{2}$ and other semiconducting materials.