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

The enhancement mechanism of piezoelectric properties 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/d epsilon) of the internal parameter, were improved by the addition of Mg + X into AlN. The decrease in C-33 and the increase in du/d epsilon that were observed in Mg + Xcodoped 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.