Fig. 4: First-principles studies of the EO coefficients of ScAlN.
From: Unveiling the Pockels coefficient of ferroelectric nitride ScAlN
a Comparison between experiment and calculated total EO coefficient r13 and r33. Error bars represent estimated 2σ uncertainties. b Separated electronic, ionic and piezoelectric contributions to r13 coefficient. c Mode-by-mode decomposition of \({r}_{13}^{{{{\rm{ion}}}}}\) in AlN and Sc0.5Al0.5N, with their corresponding vibrational eigenmodes depicted in (e). Phonon modes are labeled in ascending order of frequency. \({\alpha }_{11}^{m}\) and pm,3 are components of the Raman susceptibility and mode polarity induced by phonon mode m. d Atomic contributions to \({\alpha }_{11}^{m}\), pm,3 and Born effective charge \({Z}_{\gamma,33}^{*}\) for the dominant phonon modes (A1(TO) modes in AlN and ScAlN2). e Atomic vibrations of A1(TO) modes in AlN (625 cm−1) and in ScAlN2 (540 cm−1). Eigenvectors of phonon modes are represented by arrows.
