title: Piezoelectric coefficients and spontaneous polarization of ScAlN.
abstract: We present a computational study of spontaneous polarization and piezoelectricity in Sc(x)Al(1-x)N alloys in the compositional range from x = 0 to x = 0.5, obtained in the context of density functional theory and the Berry-phase theory of electric polarization using large periodic supercells. We report composition-dependent values of piezoelectric coefficients e(ij), piezoelectric moduli d(ij) and elastic constants C(ij). The theoretical findings are complemented with experimental measurement of e33 for a series of sputtered ScAlN films carried out with a piezoelectric resonator. The rapid increase with Sc content of the piezoelectric response reported in previous studies is confirmed for the available data. A detailed description of the full methodology required to calculate the piezoelectric properties of ScAlN, with application to other complex alloys, is presented. In particular, we find that the large amount of internal strain present in ScAlN and its intricate relation with electric polarization make configurational sampling and the use of large supercells at different compositions necessary in order to accurately derive the piezoelectric response of the material.
authors.affiliation: Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland. COMP Centre of Excellence in Computational Nanoscience, Department of Applied Physics, Aalto University, 02150 Espoo, Finland.
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Caro
authors.forename: Siyuan
authors.initials: S
authors.lastname: Zhang
authors.forename: Tommi
authors.initials: T
authors.lastname: Riekkinen
authors.forename: Markku
authors.initials: M
authors.lastname: Ylilammi
authors.forename: Michelle A
authors.initials: MA
authors.lastname: Moram
authors.forename: Olga
authors.initials: O
authors.lastname: Lopez-Acevedo
authors.forename: Jyrki
authors.initials: J
authors.lastname: Molarius
authors.forename: Tomi
authors.initials: T
authors.lastname: Laurila