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.

Large piezoelectric response of quarternary wurtzite nitride alloys and its physical origin from first principles

“…A (3 × 3 × 3) Monkhorst-Pack k mesh and 400-eV plane-wave energy cutoff was used in all calculations. The piezoelectric coefficients and elastic constants of a 4 × 4 × 2 B4-AlN supercell are converged with respect to the k mesh and energy cutoff to within 5% of previous works [23,24].…”

“…This approximation will provide a lower bound of d 33 because of the signs and magnitudes of the in-plane parameters, for ScAlN parameters; see Ref. [24]. The approximation is further motivated by the rigidity of the substrate lattice preventing the thin films to change in-plane geometry, thus reducing in-plane contributions to the piezoelectric response.…”

Theoretical and experimental study of ScAlN/Sapphire structure based SAW sensor

“…Table 1 summarizes the main data collected in published works concerning the ScAlN. It has been demonstrated by calculation [10] and experimentally [9] that the elastic constants C ij vary linearly with the concentration of Scandium. In order to obtain a complete set of constants for lower concentrations, we have determined these constants by extrapolation considering those of the pure AlN (x = 0%) and the available ones (generally x = 43%).…”

“…If theses constants are now well established for Sapphire and AlN, it is not the case for ScAlN. Several sets of constants could be found in literature [7][8][9][10][11] and these constants are of course depending on the concentration of scandium in the film. These constants, determined by different experimental methods or by calculation, show a strong scatter, making the choice of the accurate set difficult.…”

Composition measurement of epitaxial ScxGa1−xN films

“…This change is correlated with a decrease in the c/a lattice parameter ratio of the Sc x Ga 1-x N alloy as a function of increasing Sc content, leading to a phase transition from the wurtzite to the rock-salt structure (predicted to occur around x = 0.66 [10,14], although in practice spinodal decomposition or other forms of decomposition of the alloy may occur before such high Sc contents are reached). Other important physical properties relevant to devices, for instance the piezoelectric coefficients, are also composition dependent [19,20,36]. However, conventional optical absorption measurements of the band gaps are not reliable, as the values obtained can vary by more than 1 eV for the same composition, depending on the types and densities of the defects in the films [18].…”