Domain–wall contribution to the piezoelectric response of epitaxial ferroelectric thin films

Domain–wall contribution to the longitudinal piezoelectric coefficient d33 is calculated theoretically for prepolarized tetragonal ferroelectric thin films epitaxially grown on cubic substrates. To that end, translational vibrations of ferroelastic 90° domain walls induced by a weak measuring electric field are analyzed in the typical case of a laminar c/a/c/a domain structure. The average orthogonal displacement of the film free surface caused by collective domain–wall movements is calculated by the method of effective dislocations. On this base the domain–wall contribution Δd33 to the converse piezoelectric effect is evaluated and shown to be substantial in common heterostructures.