JOURNAL OF APPLIED PHYSICS 107, 114105 2010
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program, Department of Chemical, Materials, and Biomolecular
Engineering and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 16 December 2009; accepted 13 March 2010; published online 3 June 2010
We develop a nonlinear thermodynamic model to predict the phase stability of ultrathin epitaxial
001 -oriented ferroelectric PbZr1−xTixO3 PZT films with x=1.0, 0.9, 0.8, and 0.7 on substrates
which induce anisotropic in-plane strains. The theoretical formalism incorporates the relaxation by
misfit dislocations at the film deposition temperature, the possibility of formation of ferroelectric
polydomain structures, and the effect of the internal electric field that is generated due to incomplete
charge screening at the film-electrode interfaces and the termination of the ferroelectric layer. This
analysis allows the development of misfit strain phase diagrams that provide the regions of stability
of monodomain and polydomain structures at a given temperature, film thickness, and composition.
It is shown that the range of stability for rotational monodomain phase is markedly increased in
comparison to the same ferroelectric films on isotropic substrates. Furthermore, the model finds a
strong similarity between ultrathin PbTiO3 and relatively thicker PZT films in terms of phase
stability. The combinations of the in-plane misfit strains that yield a phase transition sequence that
results in a polarization rotation from the c-phase polarization parallel to the 001 direction in the
film to the r-phase, and eventually to an in-plane polarization parallel to the 110 direction the
aa-phase is determined to be the path with the most attractive dielectric and piezoelectric
coefficients resulting in enhancements of 10 to 100 times in the dielectric permittivity and
piezoresponse compared to bulk tetragonal ferroelectrics of the same PZT composition. © 2010
American Institute of Physics. doi:10.1063/1.3386465
Sunday, October 3, 2010
Misfit strain–film thickness phase diagrams and related electromechanical properties of epitaxial ultra-thin lead zirconate titanate films
Acta Materialia 58 (2010) 823–835
Q.Y. Qiu , R. Mahjoub, V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
S.P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
Received 19 March 2009; received in revised form 7 August 2009; accepted 29 September 2009
Available online 24 October 2009
Abstract
The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr1–xTixO3 (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization
field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities e11 and e33, as well as the out-of-plane piezoelectric coefficients d33 for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.
2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Ferroelectricity; Thin films; Phase transformations; Electroceramics; Dielectrics
Q.Y. Qiu , R. Mahjoub, V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
S.P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, CT 06269, USA
Received 19 March 2009; received in revised form 7 August 2009; accepted 29 September 2009
Available online 24 October 2009
Abstract
The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr1–xTixO3 (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization
field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities e11 and e33, as well as the out-of-plane piezoelectric coefficients d33 for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.
2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Ferroelectricity; Thin films; Phase transformations; Electroceramics; Dielectrics
Film thickness versus misfit strain phase diagrams for epitaxial PbTiO3 ultrathin ferroelectric films
PHYSICAL REVIEW B 78, 064117 2008
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 1 June 2008; revised manuscript received 14 July 2008; published 27 August 2008
We present a full scale nonlinear thermodynamic model based on a Landau-Ginzburg-Devonshire formalism and the theory of dense polydomain structures in a multiparameter space to predict the phase stability of 001 oriented PbTiO3 epitaxial thin films as a function of film thickness and epitaxial strain. The developed methodology, which accounts for electrostatic boundary conditions as well as the formation of misfit dislocations and polydomain structures, produces a thickness-strain phase stability diagram where it finds that the rotational phases the so-called r and ac phases in epitaxial PbTiO3 are possible only in a very small window. We find that for experimentally used thickness or strains or both that often fall outside this window, the film is in either single phase tetragonal c phase or in a c/a/c/a polydomain state; this explains why rotational polar domains are rarely observed in epitaxial ferroelectric thin films.
DOI: 10.1103/PhysRevB.78.064117
PACS number s : 77.80.Bh, 77.84.Dy
Q. Y. Qiu and V. Nagarajan
School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
S. P. Alpay
Materials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06269, USA
Received 1 June 2008; revised manuscript received 14 July 2008; published 27 August 2008
We present a full scale nonlinear thermodynamic model based on a Landau-Ginzburg-Devonshire formalism and the theory of dense polydomain structures in a multiparameter space to predict the phase stability of 001 oriented PbTiO3 epitaxial thin films as a function of film thickness and epitaxial strain. The developed methodology, which accounts for electrostatic boundary conditions as well as the formation of misfit dislocations and polydomain structures, produces a thickness-strain phase stability diagram where it finds that the rotational phases the so-called r and ac phases in epitaxial PbTiO3 are possible only in a very small window. We find that for experimentally used thickness or strains or both that often fall outside this window, the film is in either single phase tetragonal c phase or in a c/a/c/a polydomain state; this explains why rotational polar domains are rarely observed in epitaxial ferroelectric thin films.
DOI: 10.1103/PhysRevB.78.064117
PACS number s : 77.80.Bh, 77.84.Dy
Band structure of surface states and resonances for clean Cu(110) surface
Surface Science 601 (2007) 5779–5782
M.N. Read *, Q.Y. Qiu
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
Available online 30 June 2007
Abstract
We have used the layer KKR method to calculate the Shockley and Rydberg surface states and resonances for Cu(110) for a given model of the surface potentials. This method has not been used before to predict all of the surface band structure for the energy range from the bottom of the conduction band to 7 eV above the vacuum level. The previous methods that used only local electron interactions in ab initio calculations could not produce the Rydberg surface barrier bands while those relying on nearly-free-electron parameterisation of bands could not deal with d-bands.
2007 Elsevier B.V. All rights reserved.
Keywords: Cu(110) surface electronic states; Surface electronic structure calculations; Shockley and Rydberg surface bands; Layer-by-layer KKR
scattering method
M.N. Read *, Q.Y. Qiu
School of Physics, University of New South Wales, Sydney, NSW 2052, Australia
Available online 30 June 2007
Abstract
We have used the layer KKR method to calculate the Shockley and Rydberg surface states and resonances for Cu(110) for a given model of the surface potentials. This method has not been used before to predict all of the surface band structure for the energy range from the bottom of the conduction band to 7 eV above the vacuum level. The previous methods that used only local electron interactions in ab initio calculations could not produce the Rydberg surface barrier bands while those relying on nearly-free-electron parameterisation of bands could not deal with d-bands.
2007 Elsevier B.V. All rights reserved.
Keywords: Cu(110) surface electronic states; Surface electronic structure calculations; Shockley and Rydberg surface bands; Layer-by-layer KKR
scattering method
Theoretical investigation of polarization scaling in ultrathin epitaxial PbZrxTi1−xO3 films
JOURNAL OF APPLIED PHYSICS 102, 104113 2007
Q. Y. Qiu and V. Nagarajana
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
Received 21 August 2007; accepted 27 September 2007; published online 29 November 2007
We present a theoretical analysis of the scaling of the polarization and the static dielectric susceptibility through a mean-polarization approach for ultrathin epitaxial PbZrxTi1−xO3 thin films. We use the traditional Euler-Lagrangian framework applied to a Landau-Ginzburg-Devonshire LGD nonlinear thermodynamic treatment. The novelty of our approach is that the model hinges on using experimentally measured correlation lengths and temperature scaling relationships to give the size-dependent expansion parameters of the nonlinear thermodynamic potential. These are then used in a Taylor series expansion of the polarization at the center of the film. We show that this method is able to correctly predict experimentally observed scaling without the need for the so-called extrapolation length which is impossible to measure experimentally . Furthermore, as no implicit correlation between the correlation length and the coefficient of the gradient term in the LGD potential g11 is assumed, the model thus involves fully experimentally measurable parameters and their systematic temperature dependence rather than implicit assumptions. The model finds that the Curie temperature in ultrathin films is more sensitive to epitaxial strain as compared to the polarization and that the critical thickness is strongly dependent on the “temperature-epitaxial strain” parameter space. Interestingly, while it finds that at lower temperatures the depolarization field does play a strong role in the thickness dependence as well as spatial profile of the polarization, with increasing temperature, a significant weakening of the role of depolarization fields occurs. Consequently the interface-induced suppression is lower and, as a result, the polarization profile is more homogenous at higher temperatures. This indicates that systematic temperature dependent studies are fundamental to further understanding of size effects i ferroelectrics.
© 2007 American Institute of Physics. DOI: 10.1063/1.2809334
Q. Y. Qiu and V. Nagarajana
School of Materials Science and Engineering, University of New South Wales, Sydney,
New South Wales 2052, Australia
Received 21 August 2007; accepted 27 September 2007; published online 29 November 2007
We present a theoretical analysis of the scaling of the polarization and the static dielectric susceptibility through a mean-polarization approach for ultrathin epitaxial PbZrxTi1−xO3 thin films. We use the traditional Euler-Lagrangian framework applied to a Landau-Ginzburg-Devonshire LGD nonlinear thermodynamic treatment. The novelty of our approach is that the model hinges on using experimentally measured correlation lengths and temperature scaling relationships to give the size-dependent expansion parameters of the nonlinear thermodynamic potential. These are then used in a Taylor series expansion of the polarization at the center of the film. We show that this method is able to correctly predict experimentally observed scaling without the need for the so-called extrapolation length which is impossible to measure experimentally . Furthermore, as no implicit correlation between the correlation length and the coefficient of the gradient term in the LGD potential g11 is assumed, the model thus involves fully experimentally measurable parameters and their systematic temperature dependence rather than implicit assumptions. The model finds that the Curie temperature in ultrathin films is more sensitive to epitaxial strain as compared to the polarization and that the critical thickness is strongly dependent on the “temperature-epitaxial strain” parameter space. Interestingly, while it finds that at lower temperatures the depolarization field does play a strong role in the thickness dependence as well as spatial profile of the polarization, with increasing temperature, a significant weakening of the role of depolarization fields occurs. Consequently the interface-induced suppression is lower and, as a result, the polarization profile is more homogenous at higher temperatures. This indicates that systematic temperature dependent studies are fundamental to further understanding of size effects i ferroelectrics.
© 2007 American Institute of Physics. DOI: 10.1063/1.2809334
Subscribe to:
Posts (Atom)