Dielectric tunability of graded barium strontium titanate multilayers: Effect of thermal strains

A thermodynamic model was developed to analyze the effect of the difference in the thermal expansion coefficient (TEC) of a multilayered barium strontium titanate Ba1-ySryTiO3 (BST) ferroelectric heterostructure and a passive substrate on the dielectric properties by taking into account electrostatic and electromechanical interactions between the ferroelectric layers. Results show that the dielectric constant and tunability can be maximized by minimizing the TEC mismatch. Furthermore, lower processing temperatures lead to lower thermal strains and thus to better dielectric properties. We also provide a numerical analysis describing the effect of thermal strains on dielectric properties of a compositionally graded trilayer consisting of BST 60/40, BST 75/25, and BST 90/10 on a variety of substrates including Si, sapphire (alpha-Al2O3), SrTiO3, MgO, and LaAlO3. The multilayer BST heterostructure on Si is expected to experience high in-plane tensile strains due to the large TEC mismatch, resulting in dielectric permittivities and tunabilities lower compared to the same multilayer on SrTiO3 or LaAlO3 for which there is a better TEC match. For BST multilayers on MgO, SrTiO3, Si, and sapphire, higher processing temperatures lead to lower dielectric response and tunability.