Phonon-mode hardening in epitaxial PbTiO 3 ferroelectric thin films

Using (110) ${\mathrm{NdGaO}}_{3}$ wafers as the lattice matched substrates, ${\mathrm{PbTiO}}_{3}$ thin films have been epitaxially grown by metal-organic chemical vapor deposition under reduced pressure. Highly resolved Raman spectra of the thin films have been recorded by a grazing-angle scattering technique. The E(1TO) mode of the epitaxial film has been observed to have a 7-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ upward shift compared to the bulk ${\mathrm{PbTiO}}_{3}$ single crystal, which is different from the soft-mode behavior observed in ${\mathrm{PbTiO}}_{3}$ ultrafine powder and polycrystalline thin films. This transverse optical mode upshift phenomenon is attributable to the residual in-plane compressive stress in the epitaxial thin film caused by the film-substrate interaction. This phonon-mode-shift phenomenon provides a method to estimate the residual stresses existing in a ferroelectric thin film.