Domain configurations due to multiple misfit relaxation mechanisms in epitaxial ferroelectric thin films. I. Theory

Possible mechanisms for strain relaxation in ferroelectric thin films are developed. The models are applicable to tetragonal thin film ferroelectrics grown epitaxially on (001) cubic single crystal substrates. We assume growth at temperatures in excess of the Curie temperature (Tc). The extent of strain accommodation by misfit dislocations is considered at the growth temperature (Tg). On cooling to Tc, further misfit dislocation generation is possible due to differences in thermal expansion behavior of the film and substrate. During the paraelectric to ferroelectric transition (PE→FE) additional strains develop in the film. The total strain for the FE phase may be relieved either by further misfit generation or by domain formation. We have developed temperature dependent stability maps that predict the stable domain structure that forms during the PE→FE transition. The stability maps incorporate the role of the following parameters: (i) substrate lattice parameter, (ii) differential thermal expansion characteristics between the film and substrate, (iii) cooling rate, and (iv) depolarizing fields and electrode geometry. Further, the role of dislocation stabilization of domain patterns is discussed.