ENERGETICS AND GEOMETRY OF 90-DEGREES DOMAIN-STRUCTURES IN EPITAXIAL FERROELECTRIC AND FERROELASTIC FILMS

Statics of 90 degrees domain structures formed in a thin tetragonal hi m epitaxially grown on a cubic substrate is studied theoretically on t he basis of a rigorous solution of the associated elasticity problem. Inhomogeneous internal stresses existing in the strained polydomain ep itaxy are calculated by the method of fictitious dislocations distribu ted along domain boundaries and the film/substrate interface. The calc ulation properly takes into account the influence of the film free sur face on the field of internal stresses. For both possible periodic lam inar structures, the energies of elastic strain fields existing in the film and the substrate are evaluated. These results are used to compu te the equilibrium geometric parameters of periodic domain structures that minimize the total internal energy of a polydomain epitaxy. The d ependencies of the equilibrium parameters on the film thickness and th e relative misfit strain between the substrate and film are described. By comparing the minimum internal energies associated with various do main configurations, a dia,sram of equilibrium domain patterns is deve loped. In the range of relative misfit strains lower than some critica l value. two threshold film thickness exist, separating three stabilit y regions of domain patterns which correspond to a monovariant film an d two periodic domain structures. In the rest of the diagram, a patter n consisting of equivalent domains with the tetragonal axes parallel t o the interface is stable, irrespective of the film thickness. (C) 199 5 American Institute of Physics.