Nanomechanics of Ferroelectric Thin Films and Heterostructures
The focus of this chapter is to provide basic concepts of how external strains/stresses altering ferroelectric property of a material and how to evaluate quantitatively the effect of strains/stresses on phase stability, domain structure, and material ferroelectric properties using the phase-field method. The chapter starts from a brief introduction of ferroelectrics and the Landau-Devinshire description of ferroelectric transitions and ferroelectric phases in a homogeneous ferroelectric single crystal. Due to the fact that ferroelectric transitions involve crystal structure change and domain formation, strains and stresses can be produced inside of the material if a ferroelectric transition occurs and it is confined. These strains and stresses affect in turn the domain structure and material ferroelectric properties. Therefore, ferroelectrics and strains/stresses are coupled to each other. The ferroelectric-mechanical coupling can be used to engineer the material ferroelectric properties by designing the phase and structure. The followed section elucidates calculations of the strains/stresses and elastic energy in a thin film containing a single domain, twinned domains to complicated multidomains constrained by its underlying substrate. Furthermore, a phase field model for predicting ferroelectric stable phases and domain structure in a thin film is presented. Examples of using substrate constraint and temperature to obtain interested ferroelectric domain structures in BaTiO3 films are demonstrated b phase field simulations.