Strain gradients in epitaxial ferroelectrics

Abstract

X-ray analysis of ferroelectric thin layers of ${\mathrm{Ba}}_{1∕2}{\mathrm{Sr}}_{1∕2}\mathrm{Ti}{\mathrm{O}}_{3}$ with different thicknesses reveals the presence of strain gradients across the films and allows us to propose a functional form for the internal strain profile. We use this to calculate the influence of strain gradient, through flexoelectric coupling, on the degradation of the ferroelectric properties of films with decreasing thickness, in excellent agreement with the observed behavior. This paper shows that strain relaxation can lead to smooth, continuous gradients across hundreds of nanometers, and it highlights the pressing need to avoid such strain gradients in order to obtain ferroelectric films with bulklike properties.