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EFFECTS OF ELECTRIC FIELD ON PIEZOELECTRIC RESPONSES OF FERROELECTRIC THIN FILMS
Roytburd, Alexander L
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The results of theoretical and experimental studies of the piezoeffect in thin ferroelectric films constrained by substrates are presented. The elastic interactions between the film and the substrate has been calculated and proven to be a key factor in determining total piezoresponse of thin film. Thermodynamic theory is employed to explain the electric field dependence of piezoelectric properties of a single domain PbZrxTi1-xO3 (PZT) material. The strong nonlinearity of converse piezoelectric coefficient under large external electric field is proven to be intrinsic both in bulk crystal and in epitaxial thin films of tetragonal PZT. The tunability of piezoelectric responses by external electric field and its dependence on film/substrate misfit and elastic compliance of thin films are characterized quantitatively. The theoretical predictions are in good agreement with the experimental results of piezoresponse force microscopy. It is shown that under an applied electric field, 180° ferroelectric domains act as elastic domains due to the converse piezoelectric effect. The effective dielectric and piezoelectric responses of thin films are determined by interdomain elastic interactions in addition to the substrate clamping effects. Characteristics of the piezoelectric loops of thin ferroelectric films have been explained from this point of view. Experimental proof of the existence of strong interdomain elastic interactions has been obtained via piezoresponse force microscopy. It has been demonstrated that new 90° elastic domains are observed in epitaxial PZT 20/80 (x=0.2) thin films in vicinity of 180° domains, which are formed under strong local electric field created by the AFM tip. The area of internal stress arises under a conductive tip due to opposite signs of the converse piezoelectric strains in the switched 180° domain and the unswitched film. The formation of 90° domains leads to the relaxation of the internal stress. The necessary conditions for realization of this relaxation mechanism are presented. While most of studies on piezoresponse of thin films are based on the assumption that the substrate is rigid, we have found that elasticity and thickness of the substrate play a significant role in the converse piezoresponse of the films and therefore cannot be neglected. Through the theoretical analysis based on different boundary conditions, it has been shown that the elastic deformation of the substrate contributes positively to the total piezodisplacement, while the film/substrate bending can give much larger negative deflections.