Thermodynamics of polydomain heterostructures. III. Domain stability map

Abstract

A map showing regions of stability of possible domain structures and relative fractions of domains in a polytwin structure is developed for epitaxial heterostructures with active layers which undergo a cubic–tetragonal or a tetragonal–orthorhombic transformation. This map, which is also applicable to epitaxial film–substrate systems, shows the dependence of the polytwin structure on misfit strain, lattice parameters of the product phase, and mechanical stress. A uniaxial stress field applied during cooling down from the growth temperature strongly affects the domain structure selection and perfect single-domain structures may be obtained with such fields. For polytwin layers with thicknesses close to the critical thickness for domain formation, microstresses must be taken into consideration and the domain stability map is modified accordingly. Misfit dislocation generation at the deposition temperature is taken into account through a temperature dependent effective substrate lattice parameter. As examples, PbTiO3(001) films grown on MgO(001) and SrTiO3(001) substrates are analyzed. Theoretical predictions are in good agreement with experimental results from the literature. The maps for epitaxial BaTiO3(001) films grown on various substrates are also included. Experimental observations for YBa2Cu3O7−x films strongly support the ideas developed in this paper.

Monodomain strained ferroelectricPbTiO3thin films: Phase transition and critical thickness study

“…For instance, the model of Koukhar et al 9 for dense domain structures predicts an equilibrium volume fraction of c domains, i.e., having the c axis perpendicular to the surface, of 80% in PbTiO 3 ͑PTO͒ films grown on ͑001͒-SrTiO 3 ͑STO͒ substrates. However, the models of Pertsev et al 7 and Alpay and Roytburd 8 for the same strain predict the formation of completely c-oriented films.…”

“…Also in the related use of the effective substrate lattice parameter ͑b ‫ء‬ ͒, accounting for the reduced mismatch a film experiences from the substrate due to introduction of a misfit dislocation density, the MB model became influential. [6][7][8][9]11,14 This model predicts for PTO on ͑001͒-STO a relatively small critical thickness of the order of only 10 nm. 6,14 However, it has been shown that the MB model works well for metals but strongly underestimates the critical thickness in semiconductor films, particularly at relatively low strains.…”

“…2,3,6,[8][9][10] Domain structures arise when this phase is cooled through T c . In such a case the models of Koukhar et al 9 and Li et al 10 can be applied.…”

“…[2][3][4][5] Several theoretical models were developed, predicting the effect of substrate constraints on domain structures in ferroelectric films. [6][7][8][9][10][11] Clearly, in order to apply these models a detailed understanding of the precise boundary conditions is required. This is a subject area that is still shrouded with considerable confusion.…”

Effect of elastic domains on electromechanical response of epitaxial ferroelectric films with a three-domain architecture

“…The elastic domain structure in epitaxial films has been studied extensively in theory [11,[18][19][20][21][22] and in experiment [12,13,23] during the last two decades. However, the theoretical work, including the comprehensive analysis based on homogeneous theory [10,18], construction of domain stability map based on theories of elastic domains and coherent phases [19], phase field modeling [11], and exact analytical solutions [20,21], mainly concentrated on elastic domain assemblies consisting of two domain variants (polytwins), except a few by Slutsker et al [22].…”