Effects of lattice parameters on piezoelectric constants in wurtzite materials: A theoretical study using first-principles and statistical-learning methods

Longitudinal piezoelectric constant (e33) values of wurtzite materials, which are listed in a structure database, are calculated and analyzed by using first-principles and statistical learning methods. It is theoretically shown that wurtzite materials with high e33 generally have small lattice constant ratios (c/a) almost independent of constituent elements, and approximately expressed as e33 ∝ c/a − (c/a)0 with ideal lattice constant ratio (c/a)0. This relation also holds for highly-piezoelectric ternary materials such as ScxAl1−xN. We conducted a search for high-piezoelectric wurtzite materials by identifying materials with smaller c/a values. It is proposed that the piezoelectricity of ZnO can be significantly enhanced by substitutions of Zn with Ca.