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

Abstract

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 (<i>d</i> ₃₃) can be increased when the elastic constant (<i>C</i> ₃₃) is decreased and the piezoelectric stress constant (<i>e</i> ₃₃) is increased. All components of <i>e</i> ₃₃, which consists of the clamped <i>e</i> ₃₃, the Born effective charge (<i>Z</i> ₃₃), and the strain sensitivity (d<i>u</i>/dε) of the internal parameter, were improved by the addition of Mg + X into AlN. The decrease in <i>C</i> ₃₃ and the increase in d<i>u</i>/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.