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Dielectric response of fully and partially depleted ferroelectric thin films and inversion of the thickness effect
This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2013 J. Phys. D: Appl. Phys. 46 125301 (http://iopscience.iop.org/0022-3727/46/12/125301) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 193.255.135.254 The article was downloaded on 19/02/2013 at 05:27
Please note that terms and conditions apply.
IOP PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 46 (2013) 125301 (11pp)
doi:10.1088/0022-3727/46/12/125301
Dielectric response of fully and partially depleted ferroelectric thin films and inversion of the thickness effect I B Misirlioglu and M Yildiz Faculty of Engineering and Natural Sciences, Sabancı University, Orhanlı/Tuzla, 34956 Istanbul, Turkey
Received 12 October 2012, in final form 15 December 2012 Published 18 February 2013 Online at stacks.iop.org/JPhysD/46/125301 Abstract We study the effect of full and partial depletion on the dielectric response characteristics of ferroelectric thin films with impurities via a computational approach. Using a thermodynamic approach along with the fundamental equations for semiconductors, we show that films with partial depletion display unique features and an enhanced dielectric response compared with those fully depleted. We find that the capacitance peak at switching can be significantly suppressed in the case of high impurity densities (>1025 m−3 ) with relatively low ionization energy, of the order of 0.5 eV. For conserved number of species in films, electromigration of ionized impurities at room temperature is negligible and has nearly no effect on the dielectric response. In films with high impurity density, the dielectric response at zero bias is enhanced with respect to charge-free films or those with relatively low impurity density (1026 impurities m−3 ), thicker films are under a heavier influence of the smearing of the transition compared with thinner ones for the same depletion charge density. What one would expect in terms of a thickness effect in charge-free films can be entirely inverted when high densities of depletion charges exist. Therefore, experimental results on size and thickness effects are highly vulnerable to misinterpretation unless one carries out measurements to estimate the depletion charge densities in ferroelectric films. One must be, however, careful in not generalizing this trend to all film thicknesses: a relatively thick film, of the order of several hundred nanometres or a micrometre or even more, with high depletion charge will have partial depletion and the depletion zone will be confined to the near-electrode regions, rendering most of the interior of the film volume nearly charge-free. Such a film might still behave similarly to a charge-free film as long as the charge-free volume is much larger than the depleted volume.
4. Conclusions The most important result we obtain from our calculations is that depletion charges, when high in density, lead to an enhancement of the dielectric response of the thicker films at a small bias with peculiar behaviour near the switching peaks despite the fact that partial or full depletion does not change the maximum ionized impurity density. Our findings imply that the thickness effect observed in stability of polarization in charge-free films can be inverted for films with moderateto-high depletion charges where thicker films have a smeared and possibly reduced Curie temperature (with respect to the charge-free films having the same thickness) contrary to what one would expect under the BCs used for polarization. The predicted increase in the dielectric constant for thicker films in this work is also in qualitative agreement with previously published experimental results. While the hystereses exhibit a shrinkage along the field axis with increasing impurity density, the slopes of the εeff –V , and therefore the C–V curves, at various bias values could be evaluated to understand whether the specimen films are fully or partially depleted. We show that fully depleted films display a rather constant slope in εeff –V plots near or away from the coercive bias while the slope of the εeff –V curves is prominently steeper than that of fully depleted films especially near coercive bias values. The reason for the latter is the partial depletion and that the depleted volume at each interface changes with applied bias rendering a significant and continuous change in polarization. In partially depleted films, the transition from a state with depletion zones at both interfaces to a state with only one depletion zone at one of the interfaces displays a characteristic kink at the relevant bias. In the case of very high impurity densities (such as >1026 m−3 ), electrical domains are stabilized at low-tomoderate bias leading to an antiferroelectric-like response of the system in the hysteresis plots. The linear D z –V region in the hystereses has a very large apparent dielectric response compared with films in the single domain state because this response comes predominantly from domain wall motion. 9
J. Phys. D: Appl. Phys. 46 (2013) 125301
I B Misirlioglu and M Yildiz
[20] Stengel M, Vanderbilt D and Spaldin N A 2009 Enhancement of ferroelectricity at metal-oxide interfaces Nature Mater. 8 392–7 [21] Okatan M B and Alpay S P 2009 Imprint in ferroelectric materials due to space charges: a theoretical analysis Appl. Phys. Lett. 95 092902 [22] Al-Saidi W and Rappe A M 2010 Density functional study of PbTiO3 nanocapacitors with Pt and Au electrodes Phys. Rev. B 82 155304 [23] Morozovska A N, Eliseev E A, Svechnikov S V, Krutov A D, Shur V Y, Borisevich A Y, Maksymovych P and Kalinin S V 2010 Finite size and intrinsic field effect on the polar-active properties of ferroelectric–semiconductor heterostructures Phys. Rev. B 81 205308 [24] Cai M Q, Zheng Y, Ma P-W and Woo C H 2011 Vanishing critical thickness in asymmetric ferroelectric tunnel junctions: first principle simulations J. Appl. Phys. 109 024103 [25] Maksymovych P et al 2012 Ultrathin limit and dead-layer effects in local polarization switching of BiFeO3 Phys. Rev. B 85 014119 [26] Watanabe Y 1998 Theoretical stability of the polarization in a thin semiconducting ferroelectric Phys. Rev. B 57 789–804 [27] Blom P W M, Wolf R M, Cillessen J F M and Krijn M P C M 1994 Ferroelectric schottky diode Phys. Rev. Lett. 73 2107–10 [28] Matsuura H 2000 Calculation of band bending in ferroelectric semiconductor New. J. Phys. 2 8.1–8.11 [29] Pintilie L and Alexe M 2005 Ferroelectric–metal heterostructures with Schottky contacts: I. Influence of the ferroelectric properties J. Appl. Phys. 98 123103 [30] Pintilie L, Boerasu I, Gomes M J M, Zhao T, Ramesh R and Alexe M 2005 Metal–ferroelectric–metal structures with Schottky contacts: II. Analysis of the experimental current–voltage and capacitance–voltage characteristics of Pb(Zr,Ti)O-3 thin films J. Appl. Phys. 98 123104 [31] He L X and Vanderbilt D 2003 First-principles study of oxygen-vacancy pinning of domain walls in PbTiO3 Phys. Rev. B 68 134103 [32] Morozovska A N and Eliseev E A 2004 Modelling of dielectric hysteresis loops in ferroelectric semiconductors with charged defects J. Phys.: Condens. Matter 16 8937–56 [33] Ren X 2004 Large electric-field-induced strain in ferroelectric crystals by point-defect-mediated reversible domain switching Nature Mater. 3 91–4 [34] Kalinin S V, Jesse S, Rodriguez B J, Chu Y H, Ramesh R, Eliseev E A and Morozovska A N 2008 Probing the role of single defects on the thermodynamics of electric-field induced phase transitions Phys. Rev. Lett. 100 155703 [35] Morozovska A N, Svechnikov S V, Eliseev E A, Rodriguez B J, Jesse S and Kalinin S V 2008 Local polarization switching in the presence of surface-charged defects: microscopic mechanisms and piezoresponse force spectroscopy observations Phys. Rev. B 78 054101 [36] Bratkovsky A M and Levanyuk A P 2000 Ferroelectric phase transitions in films with depletion charge Phys. Rev. B 61 15042–50 [37] Zubko P, Jung D J and Scott J F 2006 Space charge effects in ferroelectric thin films J. Appl. Phys. 100 114112 [38] Misirlioglu I B, Okatan M B and Alpay S P 2010 Asymmetric hysteresis loops and smearing of the dielectric anomaly at the transition temperature due to space charges in ferroelectric thin films J. Appl. Phys. 108 034105 [39] Misirlioglu I B, Cologlu H N and Yildiz M 2012 Thickness driven stabilization of saw-tooth-like domains upon phase transitions in ferroelectric thin films with depletion charges J. Appl. Phys. 111 064105
Acknowledgment IBM acknowledges the support of the Turkish Academy of ¨ Sciences (TUBA) through GEB_IP.
References [1] Kretschmer R and Binder K 1979 Surface effects on phase transitions in ferroelectric and dipolar magnets Phys. Rev. B 20 1065 [2] Bratkovsky A M and Levanyuk A P 2000 Abrupt appearance of the domain pattern and fatigue of thin ferroelectric films Phys. Rev. Lett. 84 3177–80 [3] Junquera J and Ghosez P 2003 Critical thickness for ferroelectricity in perovskite ultrathin films Nature 422 506–9 [4] Ahn C H, Rabe K M and Triscone J M 2004 Ferroelectricity at the nanoscale: local polarization in oxide thin films and heterostructures Science 303 488–91 [5] Kim D J, Jo J Y, Kim Y S, Chang Y J, Lee J S, Yoon J G, Song T K and Noh T W 2005 Polarization relaxation induced by a depolarization field in ultrathin ferroelectric BaTiO3 capacitors Phys. Rev. Lett. 95 237602 [6] Sai N, Kolpak A M and Rappe A M 2005 Ferroelectricity in ultrathin perovskite films Phys. Rev. B 72 020101 [7] Tenne D A et al 2006 Probing nanoscale ferroelectricity by ultraviolet Raman spectroscopy Science 313 1614–6 [8] Gerra G, Tagantsev A K, Setter N and Parlinski K 2006 Ionic polarizability of conductive metal oxides and critical thickness for ferroelectricity in BaTiO3 Phys. Rev. Lett. 96 107603 [9] Yacoby Y, Girshberg Y, Stern E A and Clarke R 2006 Domain structure in ultrathin ferroelectric films: analysis with a free energy model Phys. Rev. B 74 104113 [10] Nagarajan V et al 2006 Scaling of structure and electrical properties in ultrathin epitaxial ferroelectric heterostructures J. Appl. Phys. 100 051609 [11] Palova L, Chandra P and Rabe K M 2007 Modeling the dependence of properties of ferroelectric thin film on thickness Phys. Rev. B 76 014112 [12] Paul J, Nishimatsu T, Kawazoe Y and Waghmare U V 2007 Ferroelectric phase transitions in ultrathin films of BaTiO3 Phys. Rev. Lett. 99 077601 [13] Akdogan E K and Safari A 2007 Thermodynamic theory of intrinsic finite-size effects in PbTiO3 nanocrystals: I. Nanoparticle size-dependent tetragonal phase stability J. Appl. Phys. 101 064114 [14] Tagantsev A K, Gerra G and Seter N 2008 Short-range and long-range contributions to the size effect in metal–ferroelectric–metal heterostructures Phys. Rev. B 77 174111 [15] Almahmoud E, Navtsenya Y, Kornev I, Fu H X and Bellaiche L 2004 Properties of Pb(Zr,Ti)O-3 ultrathin films under stress-free and open-circuit electrical boundary conditions Phys. Rev. B 70 220102 [16] Dieguez O, Tinte S, Antons A, Bungaro C, Neaton J B, Rabe K M and Vanderbilt D 2004 Ab initio study of the phase diagram of epitaxial BaTiO3 Phys. Rev. B 69 212101 [17] Balzar D, Ramakrishnan P A and Hermann A M 2004 Defect-related lattice strain and the transition temperature in ferroelectric thin films Phys. Rev. B 70 092103 [18] Stengel M and Spaldin N A 2006 Origin of the dielectric dead layer in nanoscale capacitors Nature 443 679–82 [19] Yu J, Wu Z, Liu Z, Yan Q, Wu J and Duan W 2008 Phase diagram of ferroelectric BaTiO(3) ultrathin films under open-circuit conditions J. Phys.: Condens. Matter 20 135203
10
J. Phys. D: Appl. Phys. 46 (2013) 125301
I B Misirlioglu and M Yildiz
[49] Yang L and Dayal K 2012 Influence of strain on space charge distribution at ferroelectric thin-film free surfaces Acta Mater. 60 6457–63 [50] Scott J F 2008 Ferroelectrics go bananas J. Phys.: Condens. Matter 20 021001 [51] Bratkovsky A M and Levanyuk A P 2001 Very large dielectric response of thin ferroelectric films with the dead layers Phys. Rev. B 63 132103 [52] Hlinka J and Marton P 2006 Phenomenological model of a 90 degrees domain wall in BaTiO3 -type ferroelectrics Phys. Rev. B 74 104104 Tagantsev A K 2008 Landau expansion for ferroelectrics: which variable to use? Ferroelectrics 375 19–27 [53] Yoo H-I, Chang M-W, Oh T-S, Lee C-E and Becker K D 2007 Electrocoloration and oxygen vacancy mobility of BaTiO3 J. Appl. Phys. 102 093701 [54] Pertsev N A, Zembilgotov A G and Tagantsev A K 1998 Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films Phys. Rev. Lett. 80 1988–91 [55] Bratkovsky A M and Levanyuk A P 2009 Continuous theory of ferroelectric states in ultrathin films with real electrodes J. Comput. Theor. Nanosci. 6 465–89 [56] Levanyuk A P 2012 personal communication [57] Pintilie L, Vrejoiu I, Hesse D, LeRhun G and Alexe M 2007 Extrinsic contributions to the apparent thickness dependence of the dielectric constant in epitaxial Pb,Zr,TiO3 thin films Phys. Rev. B 75 224113
[40] Xiao Y, Shenoy V B and Bhattacharya K 2005 Depletion layers and domain walls in semiconducting ferroelectric thin films Phys. Rev. Lett. 95 247603 [41] Hong L, Soh A K, Du Q G and Li J Y 2008 Interaction of O vacancies and domain structures in single crystal BaTiO(3): two-dimensional ferroelectric model Phys. Rev. B 77 094104 [42] Zhang Y, Li J and Fang D 2010 Oxygen-vacancy-induced memory effect and large recoverable strain in a barium titanate single crystal Phys. Rev. B 82 064103 [43] Li K T and Lo V C 2005 Simulation of oyxgen vacancy induced phenomena in ferroelectric thin films J. Appl. Phys. 97 034017 [44] Misirlioglu I B and Yildiz M 2012 Polarization retention and switching in ferroelectric nanocapacitors with defects on tensile substrates Solid-State Electron. 67 38 [45] Suryanarayana P and Bhattacharya K 2012 Evolution of polarization and space charges in semiconducting ferroelectrics J. Appl. Phys. 111 034109 [46] Folkman C M, Baek S H, Nelson C T, Jang H W, Tybell T, Pan X Q and Eom C B 2010 Study of defect-dipoles in an epitaxial ferroelectric thin film Appl. Phys. Lett. 96 052903 [47] Tagantsev A K, Stolichnov I, Colla E L and Setter N 2001 Polarization fatigue in ferroelectric films: basic experimental findings, phenomenological scenarios, and microscopic features J. Appl. Phys. 90 1387–402 [48] Cockayne E and Burton B P 2004 Dipole moment of a Pb–O vacancy pair in PbTiO3 Phys. Rev. 69 144116
11
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My IOPscience
Dielectric response of fully and partially depleted ferroelectric thin films and inversion of the thickness effect
This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2013 J. Phys. D: Appl. Phys. 46 125301 (http://iopscience.iop.org/0022-3727/46/12/125301) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 193.255.135.254 The article was downloaded on 19/02/2013 at 05:27
Please note that terms and conditions apply.
IOP PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 46 (2013) 125301 (11pp)
doi:10.1088/0022-3727/46/12/125301
Dielectric response of fully and partially depleted ferroelectric thin films and inversion of the thickness effect I B Misirlioglu and M Yildiz Faculty of Engineering and Natural Sciences, Sabancı University, Orhanlı/Tuzla, 34956 Istanbul, Turkey
Received 12 October 2012, in final form 15 December 2012 Published 18 February 2013 Online at stacks.iop.org/JPhysD/46/125301 Abstract We study the effect of full and partial depletion on the dielectric response characteristics of ferroelectric thin films with impurities via a computational approach. Using a thermodynamic approach along with the fundamental equations for semiconductors, we show that films with partial depletion display unique features and an enhanced dielectric response compared with those fully depleted. We find that the capacitance peak at switching can be significantly suppressed in the case of high impurity densities (>1025 m−3 ) with relatively low ionization energy, of the order of 0.5 eV. For conserved number of species in films, electromigration of ionized impurities at room temperature is negligible and has nearly no effect on the dielectric response. In films with high impurity density, the dielectric response at zero bias is enhanced with respect to charge-free films or those with relatively low impurity density (1026 impurities m−3 ), thicker films are under a heavier influence of the smearing of the transition compared with thinner ones for the same depletion charge density. What one would expect in terms of a thickness effect in charge-free films can be entirely inverted when high densities of depletion charges exist. Therefore, experimental results on size and thickness effects are highly vulnerable to misinterpretation unless one carries out measurements to estimate the depletion charge densities in ferroelectric films. One must be, however, careful in not generalizing this trend to all film thicknesses: a relatively thick film, of the order of several hundred nanometres or a micrometre or even more, with high depletion charge will have partial depletion and the depletion zone will be confined to the near-electrode regions, rendering most of the interior of the film volume nearly charge-free. Such a film might still behave similarly to a charge-free film as long as the charge-free volume is much larger than the depleted volume.
4. Conclusions The most important result we obtain from our calculations is that depletion charges, when high in density, lead to an enhancement of the dielectric response of the thicker films at a small bias with peculiar behaviour near the switching peaks despite the fact that partial or full depletion does not change the maximum ionized impurity density. Our findings imply that the thickness effect observed in stability of polarization in charge-free films can be inverted for films with moderateto-high depletion charges where thicker films have a smeared and possibly reduced Curie temperature (with respect to the charge-free films having the same thickness) contrary to what one would expect under the BCs used for polarization. The predicted increase in the dielectric constant for thicker films in this work is also in qualitative agreement with previously published experimental results. While the hystereses exhibit a shrinkage along the field axis with increasing impurity density, the slopes of the εeff –V , and therefore the C–V curves, at various bias values could be evaluated to understand whether the specimen films are fully or partially depleted. We show that fully depleted films display a rather constant slope in εeff –V plots near or away from the coercive bias while the slope of the εeff –V curves is prominently steeper than that of fully depleted films especially near coercive bias values. The reason for the latter is the partial depletion and that the depleted volume at each interface changes with applied bias rendering a significant and continuous change in polarization. In partially depleted films, the transition from a state with depletion zones at both interfaces to a state with only one depletion zone at one of the interfaces displays a characteristic kink at the relevant bias. In the case of very high impurity densities (such as >1026 m−3 ), electrical domains are stabilized at low-tomoderate bias leading to an antiferroelectric-like response of the system in the hysteresis plots. The linear D z –V region in the hystereses has a very large apparent dielectric response compared with films in the single domain state because this response comes predominantly from domain wall motion. 9
J. Phys. D: Appl. Phys. 46 (2013) 125301
I B Misirlioglu and M Yildiz
[20] Stengel M, Vanderbilt D and Spaldin N A 2009 Enhancement of ferroelectricity at metal-oxide interfaces Nature Mater. 8 392–7 [21] Okatan M B and Alpay S P 2009 Imprint in ferroelectric materials due to space charges: a theoretical analysis Appl. Phys. Lett. 95 092902 [22] Al-Saidi W and Rappe A M 2010 Density functional study of PbTiO3 nanocapacitors with Pt and Au electrodes Phys. Rev. B 82 155304 [23] Morozovska A N, Eliseev E A, Svechnikov S V, Krutov A D, Shur V Y, Borisevich A Y, Maksymovych P and Kalinin S V 2010 Finite size and intrinsic field effect on the polar-active properties of ferroelectric–semiconductor heterostructures Phys. Rev. B 81 205308 [24] Cai M Q, Zheng Y, Ma P-W and Woo C H 2011 Vanishing critical thickness in asymmetric ferroelectric tunnel junctions: first principle simulations J. Appl. Phys. 109 024103 [25] Maksymovych P et al 2012 Ultrathin limit and dead-layer effects in local polarization switching of BiFeO3 Phys. Rev. B 85 014119 [26] Watanabe Y 1998 Theoretical stability of the polarization in a thin semiconducting ferroelectric Phys. Rev. B 57 789–804 [27] Blom P W M, Wolf R M, Cillessen J F M and Krijn M P C M 1994 Ferroelectric schottky diode Phys. Rev. Lett. 73 2107–10 [28] Matsuura H 2000 Calculation of band bending in ferroelectric semiconductor New. J. Phys. 2 8.1–8.11 [29] Pintilie L and Alexe M 2005 Ferroelectric–metal heterostructures with Schottky contacts: I. Influence of the ferroelectric properties J. Appl. Phys. 98 123103 [30] Pintilie L, Boerasu I, Gomes M J M, Zhao T, Ramesh R and Alexe M 2005 Metal–ferroelectric–metal structures with Schottky contacts: II. Analysis of the experimental current–voltage and capacitance–voltage characteristics of Pb(Zr,Ti)O-3 thin films J. Appl. Phys. 98 123104 [31] He L X and Vanderbilt D 2003 First-principles study of oxygen-vacancy pinning of domain walls in PbTiO3 Phys. Rev. B 68 134103 [32] Morozovska A N and Eliseev E A 2004 Modelling of dielectric hysteresis loops in ferroelectric semiconductors with charged defects J. Phys.: Condens. Matter 16 8937–56 [33] Ren X 2004 Large electric-field-induced strain in ferroelectric crystals by point-defect-mediated reversible domain switching Nature Mater. 3 91–4 [34] Kalinin S V, Jesse S, Rodriguez B J, Chu Y H, Ramesh R, Eliseev E A and Morozovska A N 2008 Probing the role of single defects on the thermodynamics of electric-field induced phase transitions Phys. Rev. Lett. 100 155703 [35] Morozovska A N, Svechnikov S V, Eliseev E A, Rodriguez B J, Jesse S and Kalinin S V 2008 Local polarization switching in the presence of surface-charged defects: microscopic mechanisms and piezoresponse force spectroscopy observations Phys. Rev. B 78 054101 [36] Bratkovsky A M and Levanyuk A P 2000 Ferroelectric phase transitions in films with depletion charge Phys. Rev. B 61 15042–50 [37] Zubko P, Jung D J and Scott J F 2006 Space charge effects in ferroelectric thin films J. Appl. Phys. 100 114112 [38] Misirlioglu I B, Okatan M B and Alpay S P 2010 Asymmetric hysteresis loops and smearing of the dielectric anomaly at the transition temperature due to space charges in ferroelectric thin films J. Appl. Phys. 108 034105 [39] Misirlioglu I B, Cologlu H N and Yildiz M 2012 Thickness driven stabilization of saw-tooth-like domains upon phase transitions in ferroelectric thin films with depletion charges J. Appl. Phys. 111 064105
Acknowledgment IBM acknowledges the support of the Turkish Academy of ¨ Sciences (TUBA) through GEB_IP.
References [1] Kretschmer R and Binder K 1979 Surface effects on phase transitions in ferroelectric and dipolar magnets Phys. Rev. B 20 1065 [2] Bratkovsky A M and Levanyuk A P 2000 Abrupt appearance of the domain pattern and fatigue of thin ferroelectric films Phys. Rev. Lett. 84 3177–80 [3] Junquera J and Ghosez P 2003 Critical thickness for ferroelectricity in perovskite ultrathin films Nature 422 506–9 [4] Ahn C H, Rabe K M and Triscone J M 2004 Ferroelectricity at the nanoscale: local polarization in oxide thin films and heterostructures Science 303 488–91 [5] Kim D J, Jo J Y, Kim Y S, Chang Y J, Lee J S, Yoon J G, Song T K and Noh T W 2005 Polarization relaxation induced by a depolarization field in ultrathin ferroelectric BaTiO3 capacitors Phys. Rev. Lett. 95 237602 [6] Sai N, Kolpak A M and Rappe A M 2005 Ferroelectricity in ultrathin perovskite films Phys. Rev. B 72 020101 [7] Tenne D A et al 2006 Probing nanoscale ferroelectricity by ultraviolet Raman spectroscopy Science 313 1614–6 [8] Gerra G, Tagantsev A K, Setter N and Parlinski K 2006 Ionic polarizability of conductive metal oxides and critical thickness for ferroelectricity in BaTiO3 Phys. Rev. Lett. 96 107603 [9] Yacoby Y, Girshberg Y, Stern E A and Clarke R 2006 Domain structure in ultrathin ferroelectric films: analysis with a free energy model Phys. Rev. B 74 104113 [10] Nagarajan V et al 2006 Scaling of structure and electrical properties in ultrathin epitaxial ferroelectric heterostructures J. Appl. Phys. 100 051609 [11] Palova L, Chandra P and Rabe K M 2007 Modeling the dependence of properties of ferroelectric thin film on thickness Phys. Rev. B 76 014112 [12] Paul J, Nishimatsu T, Kawazoe Y and Waghmare U V 2007 Ferroelectric phase transitions in ultrathin films of BaTiO3 Phys. Rev. Lett. 99 077601 [13] Akdogan E K and Safari A 2007 Thermodynamic theory of intrinsic finite-size effects in PbTiO3 nanocrystals: I. Nanoparticle size-dependent tetragonal phase stability J. Appl. Phys. 101 064114 [14] Tagantsev A K, Gerra G and Seter N 2008 Short-range and long-range contributions to the size effect in metal–ferroelectric–metal heterostructures Phys. Rev. B 77 174111 [15] Almahmoud E, Navtsenya Y, Kornev I, Fu H X and Bellaiche L 2004 Properties of Pb(Zr,Ti)O-3 ultrathin films under stress-free and open-circuit electrical boundary conditions Phys. Rev. B 70 220102 [16] Dieguez O, Tinte S, Antons A, Bungaro C, Neaton J B, Rabe K M and Vanderbilt D 2004 Ab initio study of the phase diagram of epitaxial BaTiO3 Phys. Rev. B 69 212101 [17] Balzar D, Ramakrishnan P A and Hermann A M 2004 Defect-related lattice strain and the transition temperature in ferroelectric thin films Phys. Rev. B 70 092103 [18] Stengel M and Spaldin N A 2006 Origin of the dielectric dead layer in nanoscale capacitors Nature 443 679–82 [19] Yu J, Wu Z, Liu Z, Yan Q, Wu J and Duan W 2008 Phase diagram of ferroelectric BaTiO(3) ultrathin films under open-circuit conditions J. Phys.: Condens. Matter 20 135203
10
J. Phys. D: Appl. Phys. 46 (2013) 125301
I B Misirlioglu and M Yildiz
[49] Yang L and Dayal K 2012 Influence of strain on space charge distribution at ferroelectric thin-film free surfaces Acta Mater. 60 6457–63 [50] Scott J F 2008 Ferroelectrics go bananas J. Phys.: Condens. Matter 20 021001 [51] Bratkovsky A M and Levanyuk A P 2001 Very large dielectric response of thin ferroelectric films with the dead layers Phys. Rev. B 63 132103 [52] Hlinka J and Marton P 2006 Phenomenological model of a 90 degrees domain wall in BaTiO3 -type ferroelectrics Phys. Rev. B 74 104104 Tagantsev A K 2008 Landau expansion for ferroelectrics: which variable to use? Ferroelectrics 375 19–27 [53] Yoo H-I, Chang M-W, Oh T-S, Lee C-E and Becker K D 2007 Electrocoloration and oxygen vacancy mobility of BaTiO3 J. Appl. Phys. 102 093701 [54] Pertsev N A, Zembilgotov A G and Tagantsev A K 1998 Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films Phys. Rev. Lett. 80 1988–91 [55] Bratkovsky A M and Levanyuk A P 2009 Continuous theory of ferroelectric states in ultrathin films with real electrodes J. Comput. Theor. Nanosci. 6 465–89 [56] Levanyuk A P 2012 personal communication [57] Pintilie L, Vrejoiu I, Hesse D, LeRhun G and Alexe M 2007 Extrinsic contributions to the apparent thickness dependence of the dielectric constant in epitaxial Pb,Zr,TiO3 thin films Phys. Rev. B 75 224113
[40] Xiao Y, Shenoy V B and Bhattacharya K 2005 Depletion layers and domain walls in semiconducting ferroelectric thin films Phys. Rev. Lett. 95 247603 [41] Hong L, Soh A K, Du Q G and Li J Y 2008 Interaction of O vacancies and domain structures in single crystal BaTiO(3): two-dimensional ferroelectric model Phys. Rev. B 77 094104 [42] Zhang Y, Li J and Fang D 2010 Oxygen-vacancy-induced memory effect and large recoverable strain in a barium titanate single crystal Phys. Rev. B 82 064103 [43] Li K T and Lo V C 2005 Simulation of oyxgen vacancy induced phenomena in ferroelectric thin films J. Appl. Phys. 97 034017 [44] Misirlioglu I B and Yildiz M 2012 Polarization retention and switching in ferroelectric nanocapacitors with defects on tensile substrates Solid-State Electron. 67 38 [45] Suryanarayana P and Bhattacharya K 2012 Evolution of polarization and space charges in semiconducting ferroelectrics J. Appl. Phys. 111 034109 [46] Folkman C M, Baek S H, Nelson C T, Jang H W, Tybell T, Pan X Q and Eom C B 2010 Study of defect-dipoles in an epitaxial ferroelectric thin film Appl. Phys. Lett. 96 052903 [47] Tagantsev A K, Stolichnov I, Colla E L and Setter N 2001 Polarization fatigue in ferroelectric films: basic experimental findings, phenomenological scenarios, and microscopic features J. Appl. Phys. 90 1387–402 [48] Cockayne E and Burton B P 2004 Dipole moment of a Pb–O vacancy pair in PbTiO3 Phys. Rev. 69 144116
11
