Journal Home > Volume 2 , Issue 1
Journal of Advanced Ceramics 2013, 2(1): 1-10 https://doi.org/10.1007/s40145-013-0044-2
Research Article | Open Access | Issue | Published: 06 April 2013

Effect of elastic domains on electromechanical response of epitaxial ferroelectric films with a three-domain architecture

Show Author's Information Jun OUYANG*,a( ),  Wei ZHANGa,  S. Pamir ALPAYb,  Alexander L. ROYTBURD*,c( )
Key Laboratory for Liquid–Solid Structural Evolution and Processing of Materials (Ministry of Education), Engineering Ceramics Laboratory, School of Materials Science and Engineering, Shandong University, Jinan 250061, Shandong, China
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs 06269, Connecticut, USA
Department of Materials Science and Engineering, University of Maryland, College Park 20742, Maryland, USA
Keywords:
ferroelectrics, domains, epitaxial films, domain wall, thermodynamics, electromechanical properties
Cite this article:
OUYANG J, ZHANG W, ALPAY SP, et al. Effect of elastic domains on electromechanical response of epitaxial ferroelectric films with a three-domain architecture. Journal of Advanced Ceramics, 2013, 2(1): 1-10. https://doi.org/10.1007/s40145-013-0044-2
Download citation
EndNote(RIS)
BibTeX

659

Views

15

Downloads

Citations

10

Crossref

N/A

WoS

10

Scopus

0

CSCD

Abstract Full text About this article

Thermodynamics of (001) epitaxial ferroelectric films completely relaxed due to the formation of elastic domains with a three-domain architecture is presented. The polydomain structure and electromechanical response of such films are analyzed for two cases corresponding to immobile and mobile elastic domain walls. It is shown that immobile elastic domains provide additional constraint which increases the mechanical and electrical clamping, thereby significantly reducing the piezoelectric and dielectric responses. On the other hand, a polydomain ferroelectric film adapts to the variations in the applied electric field by reversible domain wall displacements in the case of mobile domain walls. The comparison of the theory with experiments shows that the elastic domain walls are mobile in the fully relaxed films of ~ 1 μm thickness. In addition, if the substrate constraint is reduced via decreasing lateral size of a polydomain ferroelectric film, its piezoresponse will increase dramatically, as is experimentally verified on small islands of polydomain ferroelectric films. The general conclusions can be readily applied to other constrained polydomain films.


menu
Abstract
Full text
Outline
About this article

Effect of elastic domains on electromechanical response of epitaxial ferroelectric films with a three-domain architecture

Show Author's information Jun OUYANG*,a( ), Wei ZHANGa, S. Pamir ALPAYb, Alexander L. ROYTBURD*,c( )
Key Laboratory for Liquid–Solid Structural Evolution and Processing of Materials (Ministry of Education), Engineering Ceramics Laboratory, School of Materials Science and Engineering, Shandong University, Jinan 250061, Shandong, China
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs 06269, Connecticut, USA
Department of Materials Science and Engineering, University of Maryland, College Park 20742, Maryland, USA

Abstract

Thermodynamics of (001) epitaxial ferroelectric films completely relaxed due to the formation of elastic domains with a three-domain architecture is presented. The polydomain structure and electromechanical response of such films are analyzed for two cases corresponding to immobile and mobile elastic domain walls. It is shown that immobile elastic domains provide additional constraint which increases the mechanical and electrical clamping, thereby significantly reducing the piezoelectric and dielectric responses. On the other hand, a polydomain ferroelectric film adapts to the variations in the applied electric field by reversible domain wall displacements in the case of mobile domain walls. The comparison of the theory with experiments shows that the elastic domain walls are mobile in the fully relaxed films of ~ 1 μm thickness. In addition, if the substrate constraint is reduced via decreasing lateral size of a polydomain ferroelectric film, its piezoresponse will increase dramatically, as is experimentally verified on small islands of polydomain ferroelectric films. The general conclusions can be readily applied to other constrained polydomain films.

Keywords: ferroelectrics, domains, epitaxial films, domain wall, thermodynamics, electromechanical properties

References(38)

[1]
Roytburd AL. Martensitic transformation as a typical phase transformation in solids. Solid State Phys 1978, 33: 317–390.
DOI Google Scholar
[2]
Roytburd AL. Elastic domains and polydomain phases in solids. Phase Transitions 1993, 45: 1–34.
DOI Google Scholar
[3]
Khachaturyan AG. Theory of Structural Transformations in Solids. New York: John Wiley & Sons, 1983.
[4]
Roytburd AL, Kosenko NS. Orientational dependence of the elastic energy of a plane interlayer in a system of coherent phases. Phys Status Solidi a 1976, 35: 735–746.
DOI Google Scholar
[5]
Streiffer SK, Zielinski EM, Lairson BM, et al. Thickness dependence of the twin density in YBa2Cu3O7-δ thin films sputtered onto MgO substrates. Appl Phys Lett 1991, 58: 2171–2173.
DOI Google Scholar
[6]
Ipatova IP, Malyshkin VG, Shchukin VA. Compositional elastic domains in epitaxial layers of phase-separating semiconductor alloys. Philos Mag B 1994, 70: 557–566.
DOI Google Scholar
[7]
Kaganer VM, Jenichen B, Schippan F, et al. Strain-mediated phase coexistence in heteroepitaxial films. Phys Rev Lett 2000, 85: 341–344.
DOI Google Scholar
[8]
Kwak BS, Erbil A, Wilkens BJ, et al. Strain relaxation by domain formation in epitaxial ferroelectric thin films. Phys Rev Lett 1992, 68: 3733–3736.
DOI Google Scholar
[9]
Pompe W, Gong X, Suo Z, et al. Elastic energy release due to domain formation in the strained epitaxy of ferroelectric and ferroelastic films. J Appl Phys 1993, 74: 6012–6019.
DOI Google Scholar
[10]
Koukhar VG, Pertsev NA, Waser R. Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures. Phys Rev B 2001, 64: 214103.
DOI Google Scholar
[11]
Zhang JX, Li YL, Choudhury S, et al. Computer simulation of ferroelectric domain structures in epitaxial BiFeO3 thin films. J Appl Phys 2008, 103: 094111–094111-6.10.1063/1.2927385
DOI Google Scholar
[12]
Ouyang J, Slusker J, Levin I, et al. Engineering of self-assembled domain architectures with ultra-high piezoelectric response in epitaxial ferroelectric films. Adv Funct Mater 2007, 17: 2094–2100.
DOI Google Scholar
[13]
Nagarajan V, Roytburd A, Stanishevsky A, et al. Dynamics of ferroelastic domains in ferroelectric thin films. Nat Mater 2003, 2: 43–47.
DOI Google Scholar
[14]
Zhang W, Yuan ML, Wang XY, et al. Design and preparation of stress-free epitaxial BaTiO3 polydomain films by RF magnetron sputtering. Sci Technol Adv Mat 2012, 13: 035006.
DOI Google Scholar
[15]
Ouyang J, Roytburd AL. Theoretical modeling of coexisting tetragonal and rhombohedral heterophase polydomain structures in lead zirconate titanate ferroelectric films near the morphotropic phase boundary. Acta Mater 2006, 54: 5565–5572.
DOI Google Scholar
[16]
Ouyang J, Yang SY, Chen L, et al. Orientation dependence of the converse piezoelectric constants for epitaxial single domain ferroelectric films. Appl Phys Lett 2004, 85: 278–280.
DOI Google Scholar
[17]
Roytburd AL, Yu Y. In Twinning in Advanced Materials. Yoo MH, Wuttig M, Eds. Warrendale, PA: TMS, 1994, 221: 217.
[18]
Pertsev NA, Emelyanov AY. Domain-wall contribution to the piezoelectric response of epitaxial ferroelectric thin films. Appl Phys Lett 1997, 71: 3646–3648.
DOI Google Scholar
[19]
Alpay SP, Roytburd AL. Thermodynamics of polydomain heterostructures. Ⅲ. Domain stability map. J Appl Phys 1998, 83: 4714–4723.
DOI Google Scholar
[20]
Bratkovsky AM, Levanyuk AP. Phase transitions, stability, and dielectric response of the domain structure in ferroelectric–ferroelastic thin films. Phys Rev Lett 2001, 86: 3642–3645.
DOI Google Scholar
[21]
Bratkovsky AM, Levanyuk AP. Proper ferroelastic phase transitions in thin epitaxial films with symmetry-conserving and symmetry-breaking misfit strains. Phys Rev B 2001, 64: 134107.
DOI Google Scholar
[22]
Slutsker J, Artemev A, Roytburd AL. Engineering of elastic domain structures in a constrained layer. Acta Mater 2004, 52: 1731–1742.
DOI Google Scholar
[23]
Ma ZK, Zavaliche F, Chen L, et al. Effect of 90° domain movement on the piezoelectric response of patterned PbZr0.2Ti0.8O3/SrTiO3/Si heterostructures. Appl Phys Lett 2005, 87: 072907.
DOI Google Scholar
[24]
Roytburd AL, Yu Y. Ferroelectric and ferroelastic domain structures in epitaxial layers. Ferroelectrics 1993, 144: 137–145.
DOI Google Scholar
[25]
Slutsker J, Artemev A, Roytburd AL. Morphological transitions of elastic domain structures in constrained layers. J Appl Phys 2002, 91: 9049–9058.
DOI Google Scholar
[26]
Roytburd AL, Alpay SP, Bendersky LA, et al. Three-domain architecture of stress-free epitaxial ferroelectric films. J Appl Phys 2001, 89: 553–556.
DOI Google Scholar
[27]
Kohli M, Muralt P, Setter N. Removal of 90° domain pinning in (100) Pb(Zr0.15Ti0.85)O3 thin films by pulsed operation. Appl Phys Lett 1998, 72: 3217–3219.
DOI Google Scholar
[28]
Haun MJ, Zhuang ZQ, Furman E, et al. Thermodynamic theory of the lead zirconate–titanate solid solution system, part Ⅲ: Curie constant and sixth-order polarization interaction dielectric stiffness coefficients. Ferroelectrics 1989, 99: 45–54.
DOI Google Scholar
[29]
Roytburd AL. Thermodynamics of polydomain heterostructures. I. Effect of Macrostresses. J Appl Phys 1998, 83: 228–238.
DOI Google Scholar
[30]
Roytburd AL. Thermodynamics of polydomain heterostructures. Ⅱ. Effect of Microstresses. J Appl Phys 1998, 83: 239–245.
DOI Google Scholar
[31]
Lefki K, Dormans GJM. Measurement of piezoelectric coefficients of ferroelectric thin films. J Appl Phys 1994, 76: 1764–1767.
DOI Google Scholar
[32]
Roytburd AL, Alpay SP, Nagarajan V, et al. Measurement of internal stresses via the polarization in epitaxial ferroelectric films. Phys Rev Let 2000, 85: 190–193.
DOI Google Scholar
[33]
Fesenko EG, Gavrilyachenko VG, Semenchev AF. Domain Structure of Multiaxial Ferroelectric Crystals. Rostov-on-Don: Rostov University Press, 1990.
DOI
[34]
Nagarajan V, Stanishevsky A, Chen L, et al. Realizing intrinsic piezoresponse in epitaxial submicron lead zirconate titanate capacitors on Si. Appl Phys Lett 2002, 81: 4215–4217.
DOI Google Scholar
[35]
Bühlmann S, Dwir B, Baborowski J, et al. Size effect in mesoscopic epitaxial ferroelectric structures: Increase of piezoelectric response with decreasing feature size. Appl Phys Lett 2002, 80: 3195–3197.
DOI Google Scholar
[36]
Ganpule CS, Roytburd AL, Nagarajan V, et al. Polarization relaxation kinetics and 180° domain wall dynamics in ferroelectric thin films. Phys Rev B 2001, 65: 014101.
DOI Google Scholar
[37]
Roytburd AL, Kim TS, Su QM, et al. Martensitic transformation in constrained films. Acta Mater 1998, 46: 5095–5107.
DOI Google Scholar
[38]
Mathews SA. Ph.D.Thesis. University of Maryland, 2000.
Publication history
Copyright
Acknowledgements
Rights and permissions

Publication history

Received: 28 January 2013
Accepted: 31 January 2013
Published: 06 April 2013
Issue date: March 2013

Copyright

© The author(s) 2013

Acknowledgements

J. Ouyang would like to acknowledge the “Qi-Lu Young Scholar Fund” (Grant No. 31370080963003) from Shandong University, supported by the 985 Fund of Shandong University, and the project sponsored by SRF for ROCS, SEM (Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry). J. Ouyang and W. Zhang would like to thank the financial support of the National Natural Science Foundation of China (Project Grant Nos. 91122024 and 51002088) and the Shandong Province Outstanding Young Scientist Research Fund (Project Grant No. BS2010CL029). A. L. Roytburd is grateful to NSF-DMR (No. 0907122) for the support.

Rights and permissions

Open Access: This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Return