Abstract
A modified Weiss mean-field theory is used to study the dependence of the properties of a thin ferroelectric film on its thickness. The possibility of introducing gradient terms into the thermodynamic potential is analyzed using the calculus of variations. An integral equation is introduced to generalize the well-known Langevin equation to the case of the boundaries of a ferroelectric. An analysis of this equation leads to the existence of a transition layer at the interface between ferroelectrics or a ferroelectric and a dielectric. The permittivity of this layer is shown to depend on the electric field direction even if the ferroelectrics in contact are homogeneous. The results obtained in terms of the Weiss model are compared with the results of the models based on the correlation effect and the presence of a dielectric layer at the boundary of a ferroelectric and with experimental data.
Similar content being viewed by others
References
Y. Ishibashi, H. Orihara, and D. R. Tilley, J. Phys. Soc. Jpn. 67, 3292 (1998).
L.-H. Ong, J. Osman, and D. R. Tilley, Phys. Rev. B: Condens. Matter 63, 144109 (2001).
M. Glinchuk, E. Eliseev, and V. Stephanovich, Phys. Solid State 44(5), 953 (2002).
Z.-G. Ban, S. P. Alpay, and J. V. Mantese, Phys. Rev. B: Condens. Matter 67, 184104 (2003).
A. L. Roytburd, S. Zhong, and S. P. Alpay, Appl. Phys. Lett. 87, 092902 (2005).
N. Setter, D. Damjanovic, L. Eng, G. Fox, S. Gevorgian, S. Hong, A. Kingon, H. Kohlstedt, N. Y. Park, G. B. Stephenson, I. Stolitchnov, A. K. Taganstev, D. V. Taylor, T. Yamada, and S. Streiffer, J. Appl. Phys. 100, 051606 (2006).
A. K. Tagantsev and G. Gerra, J. Appl. Phys. 100, 051607 (2006).
I. B. Misirlioglu, G. Akcay, S. Zhong, and S. P. Alpay, J. Appl. Phys. 101, 036107 (2007).
J. H. Qiu and Q. Jiang, J. Appl. Phys. 103, 034119 (2008).
X. Lu, B. Wang, Y. Zheng, and C. Li, J. Phys. D: Appl. Phys. 41, 035303 (2008).
J. H. Qiu and Q. Jiang, J. Appl. Phys. 105, 034110 (2009).
V. M. Fridkin, R. V. Gaynutdinov, and S. Ducharme, Phys.-Usp. 53(2), 199 (2010).
K. Ishikawa and T. Uemori, Phys. Rev. B: Condens. Matter 60, 11841 (1999).
B. Strukov and A. Levanyuk, Ferroelectric Phenomena in Crystals: Physical Foundations (Springer-Verlag, Berlin, 2012).
A. Tagantsev, L. Cross, and J. Fousek, Domains in Ferroic Crystals and Thin Films (Springer-Verlag, Berlin, 2010).
M. Marvan, P. Chvosta, and J. Fousek, Appl. Phys. Lett. 86, 221922 (2005).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: L. Landau, E. Lifshitz, and L. Pitaevskii, Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Butterworth-Heinemann, Oxford, 1995).
I. Savelyev and G. Leib, Fundamentals of Theoretical Physics (Mir, Moscow, 1982).
N. Akhiezer and M. Alferieff, The Calculus of Variations (Taylor and Francis, London, 1988).
I. Tamm, Fundamentals of the Theory of Electricity (Nauka, Moscow, 1976; Mir, Moscow, 1979).
V. N. Nechaev and A. V. Shuba, Bull. Russ. Acad. Sci.: Phys. 72(9), 1230 (2008).
O. G. Vendik and S. P. Zubko, J. Appl. Phys. 82, 4475 (1997).
H. Bateman, Higher Transcendental Functions (McGraw-Hill, New York, 1955).
S. T. Davitadze, S. N. Kravchun, B. A. Strukov, B. M. Goltzman, V. V. Lemanov, and S. G. Shulman, Appl. Phys. Lett. 80, 1631 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.S. Starkov, O.V. Pakhomov, I.A. Starkov, 2013, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2013, Vol. 143, No. 6, pp. 1144–1152.
Rights and permissions
About this article
Cite this article
Starkov, A.S., Pakhomov, O.V. & Starkov, I.A. Theoretical model for thin ferroelectric films and the multilayer structures based on them. J. Exp. Theor. Phys. 116, 987–994 (2013). https://doi.org/10.1134/S1063776113060149
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776113060149