Abstract
Ferroelectric thin films have potential applications in many devices such as memories, microwaves, transduction sensors, actuators, photovoltaics, etc. The mesoscale domain structures and thus properties of ferroelectric thin films depend crucially on the amount of strain imposed upon by the underlying substrates. Phase-field method has been extensively applied to understanding the underlying physics of the experimentally observed domain structures and predicting their responses to external electrical, mechanical, thermal, and chemical stimuli. In this chapter, the fundamentals of the thin-film phase-field method and its applications in predicting the effects of strains on the phase transitions, domain structures, and the domain switching are reviewed. The prospect of using phase-field method in microstructure design and property optimization for ferroelectric thin films is discussed.
Similar content being viewed by others
References
Ahluwalia R, Tagantsev AK, Yudin P, Setter N, Ng N, Srolovitz DJ (2014) Influence of flexoelectric coupling on domain patterns in ferroelectrics. Phys Rev B 89:174105
Artemev A, Geddes B, Slutsker J, Roytburd A (2008) Thermodynamic analysis and phase field modeling of domain structures in bilayer ferroelectric thin films. J Appl Phys 103:074104
Boettinger WJ et al (2002) Phase field simulation of solidification. Ann Rev Mater Res 32:163
Bratkovsky AM, Levanyuk AP (2002) Elastic domain structure and the transition between polydomain and monodomain states in thin epitaxial films. Phys Rev B 65:094102
Britson J, Nelson C, Pan XQ, Chen LQ (2014) First-order morphological transition of ferroelastic domains in ferroelectric thin films. Acta Mater 75:188–197
Catalan G, Scott JF (2009) Physics and applications of bismuth ferrite. Adv Mater 21:2463–2485
Chao AY, Arthur AY (1975) Molecular beam epitaxy. Prog Solid State Chem 10:157–192
Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32:113
Chen LQ (2008) Phase-field method of phase transitions/domain structures in ferroelectric thin film s: a review. J Am Ceram Soc 91:1835–1844
Chen HT, Soh AK, Ni Y (2014) Phase field modeling of flexoelectric effects in ferroelectric epitaxial thin films. Acta Mech 225:1323–1333
Chen WJ, Zheng Y, Feng X, Wang B (2015) Utilizing mechanical loads and flexoelectricity to induce and control complicated evolution of domain patterns in ferroelectric nanofilms. J Mech Phys Solids 79:108–113
Choi KJ, Biegalski M, Li YL, Sharan A, Schubert J, Uecker R, Reiche P, Chen YB, Pan XQ, Gopalan V, Chen LQ, Schlom DG, Eom CB (2004) Enhancement of ferroelectricity in strained BaTiO3 thin films. Science 306:1005
Choudhury S, Li YL, Chen LQ (2005) A phase diagram for epitaxial PbZr1-xTixO3 thin films at the bulk morphotropic boundary composition. J Am Ceram Soc 88:1669–1672
Cross LE (1996) Ferroelectric materials for electromechanical transducer applications. Mater Chem Phys 43:108–115
Cross LE, Jang SJ, Newnham RE, Nomura S, Uchino K (1980) Large electrostrictive effects in relaxor ferroelectrics. Ferroelectrics 23:187–191
Diéguez O, Aguado-Puente P, Junquera J, Íñiguez J (2013) Domain walls in a perovskite oxide with two primary structural order parameters: first-principles study of BiFeO3. Phys Rev B 89:059901
Eckstein J, Bozovic I (1995) High-temperature superconducting multilayers and Heterostructures grown by atomic layer-by-layer molecular beam epitaxy. Annu Rev Mater Sci 25:679–709
Eklund CJ (2010) Ph.D. thesis, Rutgers University
Emelyanov AY, Pertsev NA, Kholkin AL (2002) Effect of external stress on ferroelectricity in epitaxial thin films. Phys Rev B 66:214108
Frey T, Chi CC, Tsuei CC, Shaw T, Bozso F (1994) Effect of atomic oxygen on the initial growth mode in thin epitaxial Cuprate films. Phys Rev B 49:3483–3491
Geneste G (2009) Landau free energy of ferroelectric crystals by thermodynamic integration. Phys Rev B 79:064101
Gránásy L et al (2006) Phase field theory of crystal nucleation and polycrystalline growth: a review. J Mater Res 21:309
Gu YJ, Rabe K, Bousquet E, Gopalan V, Chen LQ (2012) Phenomenological thermodynamic potential for CaTiO3 single crystals. Phys Rev B 85:064117
Gu YJ, Li ML, Morozovska AN, Wang Y, Eliseev EA, Gopalan V, Chen LQ (2014) Flexoelectricity and ferroelectric domain wall structures: phase-field modeling and DFT calculations. Phys Rev B 89:174111
Haeni JH, Irvin P, Chang W, Uecker R, Reiche P, Li YL, Choudhury S, Tian W, Hawley ME, Craigo B, Tagantsev AK, Pan XQ, Streiffer SK, Chen LQ, Kirchoefer SW, Levy J, Schlom DG (2004) Room-temperature ferroelectricity in strained SrTiO3. Nature 430:758
Haun MJ, Furman E, Jang SJ, Cross LE (1989a) Thermodynamic theory of the lead zirconate-titanate solid solution system, part I: phenomenology. Ferroelectrics 99:13–25
Haun MJ, Furman E, McKinstry HA, Cross LE (1989b) Thermodynamic theory of the lead zirconate-titanate solid solution system, part II: Tricritical behavior. Ferroelectrics 99:27–44
Haun MJ, Zhuang ZQ, Furman E, Jang SJ, Cross LE (1989c) Thermodynamic theory of the lead zirconate-titanate solid solution system, part III: curie constant and sixth-order polarization interaction dielectric stiffness coefficients. Ferroelectrics 99:45–54
Hong ZJ, Britson J, Hu JM, Chen LQ (2014) Local 90 degrees switching in Pb(Zr0.2Ti0.8)O3 thin film: phase-field modeling. Acta Mater 73:75–82
Hubler GK (1992) Pulsed laser deposition. MRS Bull 17:26–29
Íñiguez J, Ivantchev S, Perez-Mato JM, García A (2001) Devonshire-landau free energy of BaTiO3 from first principles. Phys Rev B 63:144103
Junquera J, Ghosez P (2003) Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422:506
Karpinsky DV, Eliseev EA, Xue F, Silibin MV, Franz A, Glinchuk MD, Troyanchuk IO, Gavrilov SA, Gopalan V, Chen LQ, Morozovska AN (2017) Thermodynamic potential and phase diagram for multiferroic bismuth ferrite (BiFeO3). npj Comput Mater 3:20
Khachaturyan AG (1983) Theory of structural transformations in solid. Wiley, New York
Kiguchi T, Aoyagi K, Ehara Y, Funakubo H, Yamada T, Usami N, Konno TJ (2011) Configuration and local elastic interaction of ferroelectric domains and misfit dislocation in PbTiO3/SrTiO3 epitaxial thin films. Sci Technol Adv Mater 12:034413
Kontsos A, Landis CM (2010) Phase-field modeling of domain structure energetics and evolution in ferroelectric thin films. J Appl Mech 77:041014
Koster G, Rijnders GJHM, Blank DHA, Rogalla H (1999) Imposed layer-by-layer growth by pulsed laser interval deposition. Appl Phys Lett 74:3729
Kouhar VG, Pertsev NA, Waser R (2001) Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures. Phys Rev B 64:214103
Kwo J, Hong M, Trevor DJ, Fleming RM, White AE, Farrow RC, Kortan AR, Short KT (1988) In situ epitaxial growth of Y1Ba2Cu3O7-x films by molecular beam epitaxy with an activated oxygen source. Appl Phys Lett 53:2683
Lee KS, Choi JH, Lee JY, Baik S (2001) Domain formation in epitaxial Pb(Zr,Ti)O3 thin films. J Appl Phys 90:4095
Li YL, Chen LQ (2006) Temperature-strain phase diagram for BaTiO3 thin films. Appl Phys Lett 88:072905
Li YL, Hu SY, Liu ZK, Chen LQ (2001) Phase-field model of domain structures in ferroelectric thin films. Appl Phys Lett 78:3878–3880
Li YL, Hu SY, Liu ZK, Chen LQ (2002a) Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films. Acta Mater 50:395–411
Li YL, Hu SY, Liu ZK, Chen LQ (2002b) Effect of electrical boundary conditions on ferroelectric domain structures in thin films. Appl Phys Lett 81:427–429
Li YL, Choudhury S, Liu ZK, Chen LQ (2003a) Effect of external mechanical constraints on the phase diagram of epitaxial PbZr1−xTixO3PbZr1−xTixO3 thin films – thermodynamic calculations and phase-field simulations. J Appl Phys 83:1608
Li YL, Hu SY, Chen LQ (2003b) Ferroelectric domain morphologies of (001)PbZr1-xTixO3 epitaxial thin films. J Appl Phys 97:034112
Li YL, Cross LE, Chen LQ (2005) A phenomenological thermodynamic potential for BaTiO3 single crystals. J Appl Phys 98:064101
Li YL, Choudhury S, Haeni JH, Biegalski MD, Vasudevarao A, Sharan A, Ma HZ, Levy J, Gopalan V, Trolier-McKinstry S, Schlom DG, Jia QX, Chen LQ (2006) Phase transitions and domain structures in strained pseudocubic (100) SrTiO3 thin films. Phys Rev B 73:184112
Li YL, Hu SY, Choudhury S, Baskes MI, Saxena A, Lookman T, Jia QX, Schlom DG, Chen LQ (2008) Influence of interfacial dislocations on hysteresis loops of ferroelectric films. J Appl Phys 104:104110
Li ML, Gu YJ, Wang Y, Chen LQ, Duan WH (2014) First-principles study of 180° domain walls in BaTiO3: mixed Bloch-Neel-Ising character. Phys Rev B 90:054106
Li YJ, Wang JJ, Ye JC, Ke XX, Gou GY, Wei Y, Xue F, Wang J, Wang CS, Peng RC, Deng XL, Yang Y, Ren XB, Chen LQ, Nan CW, Zhang JX (2015) Mechanical switching of nanoscale multiferroic phase boundaries. Adv Funct Mater 25:3405–3413
Li Q, Nelson CT, Hsu SL, Damodaran AR, Li LL, Yadav AK, McCarter M, Martin LW, Ramesh R, Kalinin SV (2017) Quantification of flexoelectricity in PbTiO3/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling. Nat Commun 8:1468
Liang LY, Li YL, Chen LQ, Hu SY, Lu GH (2009) A thermodynamic free energy function for potassium niobate. Appl Phys Lett 94:072904
Liu GQ, Zhang Q, Huang HH, Munroe P, Nagarajan V, Simons H, Hong ZJ, Chen LQ (2016) Reversible polarization rotation in epitaxial ferroelectric bilayers. Adv Mater Interfaces 3:1600444
Ma H, Chen L, Wang JL, Ma J, Boey F (2008) Strain effects and thickness dependence of ferroelectric properties in epitaxial BiFeO3 thin films. Appl Phys Lett 92:182902
Martin LW, Rappe AM (2017) Thin-film ferroelectric materials and their applications. Nat. Rev. Mater. 2:16087
Marton P, Klíč A, Paściak M, Hlinka J (2017) First-principles-based landau-Devonshire potential for BiFeO3. Phys Rev B 96:174110
Pertsev NA, Zembilgotov AG, Tagantsev AK (1998) Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films. Phys Rev Lett 80:1988
Pertsev NA, Zembilgotov AG, Tagantsev AK (1999) Equilibrium states and phase transitions in epitaxial ferroelectric thin films. Ferroelectrics 223:79–90
Pertsev NA, Kukhar VG, Kohlstedt H, Waser R (2003) Phase diagrams and physical properties of single-domain epitaxial Pb(Zr1-xTix)O3 thin films. Phys Rev B 67:054107
Pohlmann H, Wang JJ, Wang B, Chen LQ (2017) A thermodynamic potential and the temperature-composition phase diagram for single-crystalline K1-xNaxNbO3 (0≤x≤0.5). Appl Phys Lett 110:102906
Qiu QY, Mahjoub R, Alpay SP, Nagarajan V (2010) Misfit strain-film thickness phase diagrams and related electromechanical properties of epitaxial ultra-thin lead zirconate titanate films. Acta Mater. 58:823–835
Ramesh R, Luther K, Wilkens B, Hart DL, Wang E, Tarascon JM, Inam A, Wu XD, Venkatesan T (1990) Epitaxial growth of ferroelectric bismuth Titanate thin films by pulsed laser deposition. Appl Phys Lett 57:1505
Roytburd AL (1998) Thermodynamics of polydomain heterostructures. I. Effect of macrostresses. J. Appl. Phys. 83:228–238
Rupprecht G, Bell RO (1964) Dielectric constant in paraelectric perovskites. Phys Rev 135:A748
Schlom DG, Eckstein JN, Hellman ES, Streiffer SK, Harris JS, Beasley MR, Bravman JC, Geballe TH, Webb C, Dessonneck KE, Turner F (1988) Molecular beam epitaxy of layered Dy–Ba–cu–O com-pounds. Appl Phys Lett 53:1660
Schlom DG, Chen, LQ, Eom CB, Rabe KM, Streiffer SK, Triscone JM (2007) Strain tuning of ferroelectric thin films. Ann. Rev. Mater. Res. 37:589–626
Schlom DG, Chen LQ, Pan XQ, Schmehl A, Zurbuchen MA (2008) A thin film approach to engineering functionality into oxides. J. Am. Ceram. Soc. 91:2429–2454
Schlom DG, Chen LQ, Fennie CJ, Gopalan V, Muller DA, Pan XQ, Ramesh R, Uecker R (2014) Elastic strain engineering of ferroic oxides. MRS Bulletin 39:118–130
Scott JF (1988) Properties of ceramic KNO3 thin film memories. Physica B 150:160–167
Scott JF (1991) Phase transitions in ferroelectric thin films. Phase Trans 30:107–110
Seifert A, Lange FF, Speck JS (1995) Epitaxial growth of PbTiO3 thin films on (001) SrTiO3 from solution precursors. J Mater Res 10:680–691
Shen ZH, Wang JJ, Lin YH, Nan CW, Chen LQ, Shen Y (2017) High-throughput phase-field design of high-energy-density polymer nanocomposites. Adv Mater 30:1704380
Sheng G, Hu JM, Zhang JX, Li YL, Choudhury S, Jia QX, Liu ZK, Chen LQ (2008) Misfit strain-misfit strain diagram of epitaxial BaTiO3 thin films: Thermodynamic calculations and phase-field simulations. Appl. Phys. Lett. 93:232904
Shin YH, Grinberg I, Chen IW, Rappe AM (2007) Nucleation and growth mechanism of ferroelectric domain-wall motion. Nature 449:881–884
Shirokov VB, Yuzyuk YI, Dkhil B, Lemanov VV (2007) Phenomenological theory of phase transitions in epitaxial BaTiO3 thin films. Phys Rev B 75:224116
Shirokov VB, Yuzyuk YI, Dkhil B, Lemanov VV (2009) Phenomenological theory of phase transitions in epitaxial BaxSr1-xTiO3 thin films. Appl. Phys. Lett. 79:144118
Spah RJ, Hess HF, Stormer HL, White AE, Short KT (1988) Pa-rameters for in situ growth of high Tc superconducting thin films using an oxygen plasma source. Appl Phys Lett 53:441
Steinbach I (2009) Phase-field models in materials science. Model Simul Mater Sci Eng 17:073001
Sundar V, Newnham RE (1992) Electrostriction and polarization. Ferroelectrics 135:431–446
Tagantsev AK (2008) Landau expansion for ferroelectrics: which variable to use? Ferroelectrics 375:19
Tang YL, Zhu YL, Wang YJ, Wang WY, Xu YB, Ren WJ, Zhang ZD, Ma XL (2014) Atomic-scale mapping of dipole frustration at 90o charged domain walls in ferroelectric PbTiO3 films. Sci Rep 4:4115
Theis CD, Yeh J, Schlom DG, Hawley ME, Brown GW (1998) Adsorption-controlled growth of PbTiO3 by reactive molecular beam epitaxy. Thin Solid Films 325:107–114
Völker B, Marton P, Elsässer C, Kamlah M (2011a) Multiscale modeling for ferroelectric materials: a transition from the atomic level to phase-field modeling. Contin Mech Thermodyn 23:435–451
Völker B, Landis CM, Kamlah M (2011b) Multiscale modeling for ferroelectric materials: multiscale modeling for ferroelectric materials: identification of the phase-field model’s free energy for PZT from atomistic simulations. Smart Mater Struc 21:035025
Wang YL, Tagantsev AK, Damjanovic D, Setter N (2007) Landau thermodynamic potential for BaTiO3. J Appl Phys 101:104115
Wang JJ, Meng FY, Ma XQ, Xu MX, Chen LQ (2010) Lattice, elastic, polarization, and electrostrictive properties of BaTiO3 from first-principles. J Appl Phys 108:034107
Wang Y, Nelson C, Melville A, Winchester B, Shang SL, Liu ZK, Schlom DG, Pan XQ, Chen LQ (2013) BiFeO3 domain wall energies and structures: a combined experimental and density functional theory plus U study. Phys Rev Lett 110:267601
Wang JJ, Wang Y, Ihlefeld JF, Hopkins PE, Chen LQ (2016) Tunable thermal conductivity via domain structure engineering in ferroelectric thin films: a phase-field simulation. Acta Mater 111:220–231
Winchester B, Wu PP, Chen LQ (2011) Phase-field simulation of domain structures in epitaxial BiFeO3 films on vicinal substrates. Appl Phys Lett 99:052903
Wu XF, Vanderbilt D, Hamann DR (2005) Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory. Phys Rev B 72:035105
Wu PP, Ma XQ, Li YL, Gopalan V, Chen LQ (2012) Dipole spring ferroelectrics in superlattice SrTiO3/BaTiO3 thin films exhibiting constricted hysteresis loops. Appl Phys Lett 100:092905
Wu PP, Ma XQ, Li YL, Eom CB, Schlom DG, Gopalan V, Chen LQ (2015) Influence of interfacial coherency on ferroelectric switching of superlattice BaTiO3/SrTiO3. Appl Phys Lett 107:122906
Xu RJ, Zhang JL, Chen ZH, Martin LW (2015) Orientation-dependent structural phase diagrams and dielectric properties of PbZr1−xTixO3 polydomain thin films. Phys Rev B 91:144106
Xue F, Wang JJ, Sheng G, Huang E, Cao Y, Huang HH, Munroe P, Mahjoub R, Li YL, Nagarajan V, Chen LQ (2013) Phase field simulations of ferroelectrics domain structures in PbZrxTi1−xO3 bilayers. Acta Mater 61:2909–2918
Xue F, Li YJ, Gu YJ, Zhang JX, Chen LQ (2016) Strain phase separation: formation of ferroelastic domain structures. Phys Rev B 94:220101
Xue F, Ji YZ, Chen LQ (2017) Theory of strain phase separation and strain spinodal: applications to ferroelastic and ferroelectric systems. Acta Mater 133:147–159
Yamada T (1972) Electromechanical properties of oxygen-octahedra ferroelectric crystals. J Appl Phys 43:328
Zeches RJ, Rossell MD, Zhang JX, Hatt AJ, He Q, Yang CH, Kumar A, Wang CH, Melville A, Adamo C, Sheng G, Chu YH, Ihlefeld JF, Erni R, Ederer C, Gopalan V, Chen LQ, Schlom DG, Spaldin NA, Martin LW, Ramesh R (2009) A strain-driven morphotropic phase boundary in BiFeO3. Science 326:977–980
Zembilgotov AG, Pertsev NA, Böttger U, Waser R (2005) Effect of anisotropic in-plane strains on phase states and dielectric properties of epitaxial ferroelectric thin films. Appl Phys Lett 86:052903
Zhang JX, Li YL, Wang Y, Liu ZK, Chen LQ, Chu YH, Zavaliche F, Ramesh R (2007) Effect of substrate-induced strains on the spontaneous polarization of epitaxial BiFeO3 thin films. J Appl Phys 101:114105
Zhang JX, Li YL, Choudhury S, Chen LQ, Chu YH, Zavaliche F, Cruz MP, Ramesh R, Jia QX (2008) Computer simulation of ferroelectric domain structures in epitaxial BiFeO3 thin films. J Appl Phys 103:094111
Zhang W, Ouyang J, Roytburd AL (2012) Effect of thickness-mediated misfit strain on the heterophase polydomain structure of epitaxial BiFeO3 films. Script Mater 66:499–502
Zhong WL, Vanderbilt D, Rabe KM (1994) Phase transitions in BaTiO3 from first principles. Phys Rev Lett 73:1861
Acknowledgments
The research works on the domain structures and switching in ferroelectric thin films reviewed in this article have primarily been supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-07ER46417, and the works on the strain and flexoelectric effects by the National Science Foundation under DMR-1410714 and by the Penn State MRSEC, Center for Nanoscale Science, under the award NSF DMR-1420620. During the preparation of this manuscript, J. J. Wang also acknowledges the partial support for his effort from the Army Research Office under grant number W911NF-17-1-0462.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this entry
Cite this entry
Wang, JJ., Chen, LQ. (2018). Strain Control of Domain Structures in Ferroelectric Thin Films: Applications of Phase-Field Method. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_60-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-50257-1_60-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50257-1
Online ISBN: 978-3-319-50257-1
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics