Electrocaloric Effect in Multilayer Ferroelectric Structures

Introduction. Ferroelectric films are widely used for radiotechnical, microwave microelectronic, sensoric, and energy conversion purposes. Such a diverse application range demands film materials with specific electrophysical properties. For instance, while energy storage applications require materials with a high dielectric constant, energy conversion devices largely use those with a low dielectric constant. The necessary physical properties can be achieved using multicomponent ferroelectric structures, such as solid solutions, composites, and multilayer film structures. Mechanical stresses between the substrate and ferroelectric layers play an extremely important role in dielectric properties of multilayer structures.
Aim. Development of a mathematical model quantifying the ferroelectric polarization, static dielectric constant, as well as pyroelectric and electrocaloric properties of multilayered ferroelectric film structures.
Materials and methods. The presented model is based on the Landau–Ginzburg–Devonshire model (LGD) considering elasticity equations and using electric induction as the order parameter.
Results. The developed mathematical model based on LGD provides for a quantifiable description of dielectric, pyroelectric, and electrocaloric properties of layered ferroelectric structures. This model displays the effect of the thickness ratio of polycrystalline layers and grain size distribution on the dielectric properties of films.
Conclusion. The developed quantitative model demonstrates the dependence of the thickness, grain size, and stacking order of ferroelectric layers on the dielectric constant and pyroelectric coefficient of multilayered polycrystalline film structures. The presented model can be applied when optimizing the parameters of multilayer structures with respect to their application area.

1. Sigov A. S., Mishina E. D., Mukhortov V. M. Thin Ferroelectric Films: Obtaining and Perspectives Of Integration. Physics of Solid State. 2010, vol. 52, no. 4, pp. 709–717. (In Russ.)

2. Karmanenko S., Semenov A., Dedyk A., Es'kov A. V. New Approaches to Electrocaloric-Based Multilayer Cooling. Electrocaloric Materials. Berlin, Heidelberg, Springer, 2014, pp. 183–223. doi: 10.1007/978-3-642-40264-7_8

3. Valant M. Electrocaloric Materials for Future Solid-State Refrigeration Technologies. Progress in Materials Science. 2012, vol. 57, no. 6, pp. 980–1009. doi:10.1016/j.pmatsci.2012.02.001

4. Zhang G., Fan B., Zhao P., Hu Zh., Liu Y., Liu F., Jiang Sh., Zhang S., Li H., Wang Q. Ferroelectric Polymer Nanocomposites With Complementary Nanostructured Fillers for Electrocaloric Cooling with High Power Density and Great Efficiency. ACS Applied Energy Materials. 2018, vol. 1, no. 3, pp. 1344–1354. doi: 10.1021/acsaem.8b00052

5. Qian X., Han D., Zheng L., Chen J., Tyagi M., Li Q., Du F., Zheng Sh., Huang X., Zhang Sh. et al. High-Entropy Polymer Produces a Giant Electrocaloric Effect at Low Fields. Nature. 2021, vol. 600, no. 7890, pp. 664–669. doi: 10.1038/s41586-021-04189-5

6. Bai Y., Ding K., Zheng G.-P., Shi S.-Q., Qiao L. Entropy-Change Measurement of Electrocaloric Effect of BaTiO3 Single Crystal. Physica Status Solidi (a). 2012, vol. 209, no. 5, pp. 941–944. doi: 10.1002/pssa.201127695

7. Pertsev N. A., Zembilgotov A. G., Tagantsev A. K. Effect of Mechanical Boundary Conditions on Phase Diagrams of Epitaxial Ferroelectric Thin Films. Physical Review Let. 1998, vol. 80, no. 9, p. 1988. doi: 10.1103/PhysRevLett.80.1988

8. Novak N., Pirc R., Kutnjak Z. Diffuse Critical Point in PLZT Ceramics. Europhysics Let. 2013, vol. 102, no. 1, p. 17003. doi: 10.1209/0295-5075/102/17003

9. Lines M. E., Glass A. M. Principles and Applications of Ferroelectrics And Related Materials. Oxford, Oxford university press, 2001, 736 p. doi: 10.1093/acprof:oso/9780198507789.001.0001

10. Tagantsev A. K. Landau Expansion for Ferroelectrics: Which Variable to Use? Ferroelectrics. 2008, vol. 375, no. 1, pp. 19–27. doi: 10.1080/00150190802437746

11. Shirokov V. B., Yuzuk Yu. I., Dkhil B., Lemanov V. V. Fenomenological Description of Phase Transitions in Thin Films of BaTiO3. Fizika Tverdogo Tela [Physics of Solid State]. 2008, vol. 50, no. 5, pp. 889–892. (In Russ.)

12. Chen L. Q. Phase-Field Method of Phase Transitions/Domain Structures in Ferroelectric Thin Films: a Review. J. of the American Ceramic Society. 2008, vol. 91, no. 6, pp. 1835–1844. doi: 10.1111/j.1551-2916.2008.02413.x

13. Strukov B. A., Davitadze S. T., Shulman S. G., Goltzman B. V., Lemanov V. V. Clarification of Size Effects in Polycrystalline BaTiO3 Thin Films by Means of the Specific Heat Measurements: Grain Size or Film Thickness? Ferroelectrics. 2004, vol. 301, no. 1, pp. 157–162. doi: 10.1080/00150190490455674

14. Limpert E., Stahel W. A., Abbt M. Log-Normal Distributions Across The Sciences: Keys and Clues: on the Charms of Statistics, and How Mechanical Models Resembling Gambling Machines Offer a Link to a Handy Way to Characterize Log-Normal Distributions, Which Can Provide Deeper Insight into Variability and Probability-Normal or Log-Normal: That is the Question. BioScience. 2001, vol. 51, no. 5, pp. 341–352. doi: 10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2

15. Chen L. Q. APPENDIX A–Landau Free-Energy Coefficients. Physics of Ferroelectrics. 2007, vol. 105, pp. 363–372. doi: 10.1007/978-3-540-34591-6_9

16. He Y. Heat Capacity, Thermal Conductivity, and Thermal Expansion of Barium Titanate-Based Ceramics. Thermochimica Acta. 2004, vol. 419, no. 1–2, pp. 135–141. doi: 10.1016/j.tca.2004.02.008

17. Lobo R., Mohallem N. D. S., Moreira R. L. Grain-Size Effects on Diffuse Phase Transitions of Sol-Gel Prepared Barium Titanate Ceramics. J. of the American Ceramic Society. 1995, vol. 78, no. 5, pp. 1343–1346. doi: 10.1111/j.1151-2916.1995.tb08492.x

18. Starkov I. A., Anokhin A. S., Myl'nikov I. L., Mishnev M. A., Starkov A. S. Influence of Sintering Temperature on Grain Size and Electrocaloric Effect in Barium Titanate Ceramics. Physics of Solid State. 2022, vol. 64, no. 4, pp. 443–454 (In Russ.). doi: 10.21883/FTT.2022.04.52184.208

19. Arlt G., Hennings D., De With G. Dielectric Properties of Fine-Grained Barium Titanate Ceramics. J. of applied physics. 1985, vol. 58, no. 4, pp. 1619–1625. doi: 10.1063/1.336051