First principles study of the structural, electronic, and dielectric properties of amorphous HfO2

Abstract

Using first-principles density-functional theory calculations, we have investigated the structural, electronic, and dielectric properties, as well as the O vacancy formation in amorphous HfO₂. The structural properties of the generated amorphous models were analyzed via the pair correlation functions and the distribution of the atomic coordination number. The PBE0 hybrid density functional was employed for the analysis of the electronic properties and the charge transition levels of the O vacancy in amorphous HfO₂. The dielectric and vibrational properties of the generated models were analyzed using the linear response method based on the density functional perturbation theory. According to the generated structural models, the density of a-HfO₂ was 8.63 g/cm³, and the average coordination numbers of O and Hf atom were 3.06 and 6.10, respectively. The electronic band gap of a-HfO₂ was predicted to be 5.94 eV, and the static dielectric constants were calculated to be ∼ 22, both in good agreements with the experimental measurements. The computed formation energy of a neutral O vacancy in a-HfO₂ was 6.50 eV on average, which is lower than that in m-HfO₂ by 0.2–0.3 eV but remains higher than that in a-SiO₂. Unlike in m-HfO₂, the highest occupied defect levels of the negatively charged O vacancies in a-HfO₂ may lie within the band-gap region of silicon. In addition, O vacancies in the charge state q =− 2 may appear as a stable state as the electron chemical potential lies within the electronic band gap, and thus, some of the O vacancies can possess the negative-U property in a-HfO₂.