First-principles calculations of spontaneous polarization in ScAlN

The aim of this study is to obtain a systematic insight into the scandium (Sc) concentration dependence of the spontaneous polarization (P_sp) in Sc_xAl_1−xN by using first-principles calculations. From the calculated results, we observe that a structural change from a c-axis polarized wurtzite structure to a nonpolarized layered hexagonal structure takes place at x = 0.67, and the spontaneous polarization decreases nonlinearly with a change in the Sc concentration. Furthermore, we calculate the spontaneous polarizations from each cation individually and find that the spontaneous polarization from aluminum–nitrogen (Al–N) ($P_{\mathrm{sp}}^{\mathrm{AlN}}$ ) is higher than that from scandium–nitrogen (Sc–N) ($P_{\mathrm{sp}}^{\mathrm{ScN}}$ ). This difference in spontaneous polarization arising from the cationic origin is attributed to the difference in the internal parameter along the c axis ($\mathrm{\Delta }{u}_3^k$ ) based on the layered hexagonal structure.