Linear variation of aluminum nitride capacitance versus voltage induced by a piezoelectric-electrostrictive coupling

We report here the physical explanation of the unusual observed linear variation of AlN capacitance versus voltage bias: a third order coupling between piezoelectricity and electrostriction. A phenomenological model based on free energy consideration is proposed in order to implement the electrostrictive effect together with the piezoelectric one. This model allows the accurate determination of the electrostrictive coefficient of interest by two independent ways (Q13=0.094 m4 C−2), giving high confidence in the physical explanation proposed.