Effect of extrapolation length on the phase transformation of epitaxial ferroelectric thin films

Effects of extrapolation length on the phase transformation of epitaxial ferroelectric thin films on dissimilar cubic substrates have been studied on the basis of the mean-field Landau-Ginzburg-Devonshire (LGD) thermodynamic theory by taking an uneven distribution of the interior stress with thickness into account. It was found that the polarization of epitaxial ferroelectric thin films is strongly dependent on the extrapolation length of films. The physical origin of the extrapolation length during the phase transformation from paraelectric to ferroelectric was revealed in the case of ferroelectric thin films.