“…This relationship has been demonstrated to apply to a large range of wurtzite-structure piezoelectric material systems which have c/a ratios larger than 1.5, including representative wurtzite-structure oxides (BeO, MgO, ZnO), nitrides (BN, AlN, GaN, InN, Sc 0.5 Al 0.5 N, and related alloys X 0.5 Zn 0.5 N where X = Mg, Ca, Sr, and Ba), sulfides, selenides, tellurides, and iodides, and is based on an examination of the correlation between e 33 and c/a from experimental measurements and first-principles predictions. [30][31] In our More specifically, d 33 increases from 3.2 to 4.5 and 6.2 pC/N for x = 0, 0.20 and 0.36, reaches a maximum of d 33 = 6.4 pC/N for x = 0.48, and decreases to 5.9, 6.3, 6.3 pC/N for x = 0.62, 0.79, and 1.00, respectively. The inset also includes as black bar the reported d = 4.2 pC/N for AlN, [5a, 30,32] illustrating that the maximum piezoelectric response for (Ti 1−x Mg x ) 0.25 Al 0.75 N layers at x = 0.5 is 50% larger than that of the pure AlN matrix.…”