Strain effect in the problem of critical thickness for ferroelectric memory

We account for inhomogeneous strains, while calculating two characteristic thicknesses arising in the problem of critical thickness for ferroelectric memory. One of them marks the stability limit of the metastable single-domain state under zero bias voltage with respect to small fluctuations (the spinodal point of the single-domain state). The second one appears when the free energies of the single and multidomain states become equal while the latter is considered within a ‘one sinusoid’ approximation. At this thickness, the single-domain state remains metastable but one may hope that the lifetime of this state becomes considerable for memory applications. We use the Landau–Ginzburg–Devonshire approach for an elastically isotropic solid with a single electrostriction constant to illustrate this general behavior. It is found that the effect of the elastic strains is qualitatively different for free films compared to films on substrates.