Phase field simulation of misfit strain manipulating domain structure and ferroelectric properties in PbZr(1–x)TixO3 thin films

Abstract

Ferroelectric domain structures and ferroelectric properties in the hetero-epitaxially constrained ferroelectric thin films can be manipulated by substrate misfit strain. In this work, three kinds of phase structures of PbZr_{(1–<i>x</i>)}Ti<i>_x</i>O₃ thin films, including tetragonal, tetragonal- rhombohedral-mixed and rhombohedral phases, are investigated. Firstly, the ferroelectric domain structures at different substrate misfit biaxial strains are obtained by the phase-field simulation. Then we calculate the polarization-electric field hysteresis loops at different misfit strains, and obtain the coercive field, saturation polarization, and remnant polarization. In the tetragonal PbZr_{(1–<i>x</i>)}Ti<i>_x</i>O₃ (<i>x</i> = 0.8) thin film, compressive strain contributes to the formation of out-of-plane c1/c2 domain, and tensile strain favors in-plane a1/a2 domain formation. With the increase of compressive strain, the tetragonal phase and the rhombohedral phase coexist in PbZr_{(1–<i>x</i>)}Ti<i>_x</i>O₃ (<i>x</i> = 0.48) film near the morphotropic phase boundary, while the tensile strain reduces the rhombohedral domain size. In the rhombohedral PbZr_{(1–<i>x</i>)}Ti<i>_x</i>O₃ (<i>x</i> = 0.2) film, the rhombohedral domains are steady states under compressive strain and tensile strain. As the misfit strain changes from –1.0% to 1.0%, the value of the coercive field, saturation polarization and remnant polarization decrease. Among them, for tetragonal-rhombohedral mixed phase, the reductions of saturation field and remnant polarization are larger than for tetragonal phase and rhombohedral phase. The coercive field of mixed phase decreases rapidly under the compressive strain, but deceases slowly under the tensile strain. It is worth noting that the remnant polarization decreases faster than the saturation polarization in three components of ferroelectric thin film. Due to the electromechanical coupling, when <i>x</i> = 0.48 at the morphotropic phase boundary it is shown that the remnant polarization reduction is faster than those of the other two types of ferroelectric thin films, and the small coercive field is obtained in the case of large tensile strain. Therefore, tensile strain can effectively improve the energy storage efficiency in ferroelectric thin films, and the efficiency of <i>x</i> = 0.48 thin film increases significantly compared with that of <i>x</i> = 0.8 or 0.2 thin film. Both the ratio of rhombohedral/tetragonal phase and the domain size will play a significant role in ferroelectric performance. Therefore, our results contribute to the understanding of the electromechanical coupling mechanism of PbZr_{(1–<i>x</i>)}Ti<i>_x</i>O₃, and provide guidance for the experimental design of ferroelectric functional thin film materials.