First-Principles Study of Piezoelectric Properties and Bonding Analysis in (Mg, X, Al)N Solid Solutions (X = Nb, Ti, Zr, Hf)

[Image: see text] The enhancement mechanism of piezoelectric properties by codoping Mg + X (X = Nb, Ti, Zr, Hf) into aluminum nitride (AlN) was investigated by first-principles calculations. Theoretically, the piezoelectric constant (d(33)) can be increased when the elastic constant (C(33)) is decreased and the piezoelectric stress constant (e(33)) is increased. All components of e(33), which consists of the clamped e(33), the Born effective charge (Z(33)), and the strain sensitivity (du/dε) of the internal parameter, were improved by the addition of Mg + X into AlN. The decrease in C(33) and the increase in du/dε that were observed in Mg + X-codoped AlN indicate the occurrence of elastic softening which was considered to be influenced by changes in the interatomic bond in the wurtzite structure. The bonding analysis of metal–nitrogen (Me–N) pairs in the Mg + X-codoped AlN system which was carried out by crystal orbital Hamilton populations showed that the covalent bonding (Me–N) was weaker than in pure AlN. Therefore, this weaker covalent bond is considered to be one of the origins of the elastic softening. Similar phenomena were also found for Sc-doped AlN which has higher piezoelectric response than that of pure AlN.