First-principles Calculations of Raman and Infrared Spectroscopy For Phase Identification and Strain Calibration of Hafnia

Aldo Raeliarijaona; R. E. Cohen

doi:10.1063/5.0092247

paper

First-principles Calculations of Raman and Infrared Spectroscopy For Phase Identification and Strain Calibration of Hafnia

arXiv:2203.09564 · doi:10.1063/5.0092247

Abstract

Using density functional perturbation theory (DFPT) we computed the phonon frequencies, Raman and IR activities of hafnia polymorphs (P4 $_{2}$ nmc, Pca2 $_{1}$ , Pmn2 $_{1}$ , Pbca OI, brookite, and baddeleyite) for phase identification. We investigated the evolution of Raman and IR activities with respect to epitaxial strain and provide plots of frequency differences as a function of strain for experimental calibration and identification of the strain state of the sample. We found Raman signatures of different hafnia polymorphs: $ω (A_{1 g}) = 300$ cm $^{- 1}$ for P4 $_{2}$ nmc, $ω (A_{1}) = 343$ cm $^{- 1}$ for Pca2 $_{1}$ , $ω (B_{2}) = 693$ cm $^{- 1}$ for Pmn2 $_{1}$ , $ω (A_{g}) = 513$ cm $^{- 1}$ for Pbca (OI), $ω (A_{g}) = 384$ cm $^{- 1}$ for brookite, and $ω (A_{g}) = 496$ cm $^{- 1}$ for baddeleyite. We also identified the Raman $B_{1 g}$ mode, an anti-phase vibration of dipole moments, ( $ω (B_{1 g}) = 758$ cm $^{- 1}$ for OI, $ω (B_{1 g}) = 784$ cm $^{- 1}$ for brookite) as the Raman signature of antipolar Pbca structures. We calculated a large splitting between longitudinal optical (LO) and transverse optical (TO) modes ( $Δ ω_{LO-TO} (A_{1}^{z}) = 255$ cm $^{- 1}$ in Pca2 $_{1}$ , and $Δ ω_{LO-TO} (A_{1}) = 263$ cm $^{- 1}$ in Pmn2 $_{1}$ ) to the same order as those observed in perovskite ferroelectrics, and related them to the anomalously large Born effective charges of Hf atoms ( $Z^{*} (Hf) = 5.54$ ).

First-principles Calculations of Raman and Infrared Spectroscopy For Phase Identification and Strain Calibration of Hafnia

Abstract

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