Intrinsic effective piezoelectric coefficients of an epitaxial ferroelectric film

Due to substrate clamping, the effective piezoelectric coefficients of an epitaxial ferroelectric film are usually different from those of bulk materials. The modifications of intrinsic piezoelectric responses by film–substrate in-plane stresses are quantitatively illustrated for a ferroelectric film with arbitrary orientation and structure. Consequently, the intrinsic effective piezoelectric coefficients of an epitaxial ferroelectric film are generally formulated.