Optical phonon softening in strained SrTiO₃ thin film: First-principles study

The dielectric response and optical phonon of hydrostatically and anisotropically strained SrTiO₃ lattices were studied using density functional theory. A structural analysis was performed on the strained SrTiO₃ lattice. Following the structural analysis, the optical phonon frequency was calculated for a wide range of lattice distortion. The dielectric constant was calculated from the optical phonon frequency and the Born effective charges. It was found that significant optical phonon softening occurs at a certain degree of lattice distortion and a certain amount of volume change. In other words, the optical phonon frequency decreased and reached a minimum (50 cm^-1) at a specific lattice distortion (c/a=0.985) as the SrTiO₃ lattice was progressively distorted starting from the unstrained state. The phonon frequency increased as the lattice distortion was further increased. This phonon behavior, i.e., optical phonon softening, leads to a maximum dielectric constant at a certain degree of lattice distortion. The first-principles calculation on the strained SrTiO₃ shows that the strain affects the dielectric constant of the strained SrTiO₃ through the optical phonon softening (or hardening).