We have theoretically shown that doping of N atoms increases the dielectric constant of the Hf silicates, enhancing both the electronic and lattice polarization contributions. The enhancement of the lattice contribution is dominant and is attributed to low-frequency vibration modes induced by the N doping. It is found that Hf and Si ions bonded to N atoms located at O vacancies largely vibrate in the modes and play a crucial role in the enhancement. Doped N atoms are shown to also improve the electric characteristic of the silicates, elevating O vacancy levels appearing in the band gap of the silicates.
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