Research Progress in Atomistic Simulation on Ferroelectricity and Electromechanical Coupling Behavior of Nanoscale Ferroelectrics

doi:10.15541/jim20140492

Abstract

Abstract:

For nanoscale ferroelectric materials, their geometrical structures and characteristic sizes strongly affect the ferroelectricity, which are dominant factors for the reliability of functional materials in micro-electronics. Numerical simulation is an effective tool instead of the experimental method to investigate the physical properties of ferroelectrics. Particularly, when the characteristic sizes of these materials shrink to several nanometers, it may be the only option because no experimental testing system is available due to the restriction in specimen fabrication and measurement precision. In this paper, recent progresses in numerical simulations on the ferroelectricity of typical 2D, 1D and 0D nano-ferroelectrics are reviewed, especially researches on the polarization distribution, phase transition, critical size, and electromechanical coupling behavior of nanoscale ferroelectrics. Finally, the potential research emphases on numerical simulation of the nanoscale ferroelectrics are prospected.

Key words: nanoscale ferroelectrics, polarization, critical size of ferroelectricity, electromechanical coupling behavior, numerical simulation, review

CLC Number:

TM22

WANG Xiao-Yuan, YAN Ya-Bin, SHIMADA Takahiro, KITAMURA Takayuki. Research Progress in Atomistic Simulation on Ferroelectricity and Electromechanical Coupling Behavior of Nanoscale Ferroelectrics[J]. Journal of Inorganic Materials, 2015, 30(6): 561-570.

Figures/Tables 8

Fig. 1 Crystal structures of perovskite oxides ABO3 in the (a) paraelectric phase and (b) ferroelectric phase

Fig. 2 Atomic structure of ABO3 in the paraelectric, ferroelectric and antiferrodistortive phases

Fig. 3 Atomic structure of the TiO2 layer for the c(2×2) PbTiO3 surface reconstruction[45]

Fig.4 Atomic displacements in TiO2 and PbO planes, for the AFD, AFE and FE distortions of the c(2×2) surface reconstruction (a-c), and schematic representation of the polarization distortion parameters, respectively (d-f)[48]

Fig. 5 Averaged polarization, P, in (a) PbO-terminated and (b) TiO2-terminated nanowires with the cross-section of the 1×1、2×2 and 3×3 cells as a function of tensile strain, εzz[58]

Fig. 6 (a) Dipole moments, and (b)-(f) in-plane displacements of individual atoms with respect to a paraelectric reference state for a 4×4 TiO2-terminated PbTiO3 nanowire[66]

Fig. 7 (a) 2-D tetradomain vortex consisting of four domains, (b) 3-D hexadomain vortex[83]

Fig. 8 Normalized free energy vs aspect ratio for cuboidal nanodots[83]

References 84

[1]	JONA F, SHIRANE G.Ferroelectric crystals. New York: Dover, 1993: 23-72.
[2]	钟维烈. 铁电体物理学. 北京: 高等教育出版社, 1996, 7:105.
[3]	SCOTT J F. Ferroelectric Memories.Berlin; Springer, 2000: 57-91.
[4]	IKEDA T.Fundamentals of Piezoelectricity. New York: Oxford University Press, 1996: 13-35.
[5]	LINES M E, Glass A M.Principles and Applications of Ferroelectrics and Related Materials. Oxford: Clarendon, 1997: 21-45.
[6]	RAMESH R.Thin Film Ferroelectric Materials and Devices. Boston: Kluwer Academic, 1997: 4-19.
[7]	VARGHESE J, WHATMORE R W, HOLMES J D.Ferroelectric nanoparticles, wires and tubes: synthesis, characterisation and applications.J. Mater. Chem. C, 2013, 15(1): 2618-2638.
[8]	YOURDKHANI A, CARUNTU G.Characterization of the microstructural and piezoelectric properties of PbTiO3 thin films synthesized by liquid-phase deposition.J. Phys. Chem. C, 2011, 115(30): 14797-14805.
[9]	LU X, ZHANG D, ZHAO Q, et al.Large-scale sysnthesis of necklace-like single-crystalline PbTiO3 nanowires.Macromol. Rapid Commun., 2006, 27(1): 76-80.
[10]	HONG S, CHOI T, JEON J H, et al.Large resistive switching in ferroelectric BiFeO3 nano-island based switchable diodes.Advanced. Mater., 2013, 25(16): 2339-2343.
[11]	SON J Y, JUNG I.Ferroelectric PbTiO3 nanodots shattered using atomic force microscopy.J. Am. Ceram. Soc., 2012, 95(2): 480-482.
[12]	NAUMOV I I, BELLAICHE L, FU H.Unusual phase transitions in ferroelectric nanodisks and nanorods.Nature, 2004, 432(7018): 737-740.
[13]	YUN W S, URBAN J J, GU Q, et al.Ferroelectric properties of individual barium titanate nanowires investigated by scanned probe microscopy.Nano Lett., 2002, 2(5): 447-450.
[14]	JIANG B, PENG J L, BURSILL L A, et al. Size effects on ferroelectricity of ultrafine particles of PbTiO3. J. Appl. Phys., 2000, 87(7): 037601-1-4.
[15]	WU Z, COHEN R E. Pressure-induced anomalous phase transitions and colossal enhancement of piezoelectricity in PbTiO3. Phys. Rev. Lett, 2005, 95(3): 037601-1-4.
[16]	DUAN Y, QIN L, TANG G, et al. Influence of in-plane biaxial stress on the structural properties, ferroelectric response, piezoelectricity of tetragonal PbTiO3. J. Appl. Phys., 2009, 105(3): 033706-1-4.
[17]	KORNEV I, BELLAICHE L, BOUVIER P, et al. Ferroelectricity of perovskites under pressure. Phys. Rev. Lett., 2005, 95(19): 196804-1-4.
[18]	DIÉGUEZ O, RABE K M, VANDERBILT D. First-principles study of epitaxial strain in perovskites. Phys. Rev. B, 2005, 72(14): 144101-1-9.
[19]	YANG W, MA X L, WANG H T, et al.Advances in nanomechanics.Advances in Mechanics, 2002, 32(2): 161-174.
[20]	GUO T Z, GUO W L.Recent advances of numerical simulation methods in nanomechanics.Advances in Mechanics, 2002, 32(2): 175-188.
[21]	OUYANG Y F, ZHONG X P.Interatomic potentials for computer simulation of condensed matters. Advances in Mechanics, 2006, 36(3): 321-343.
[22]	HOHENBERG P, KOHN W.Inhomogeneous electron gas.Phys. Rev., 1964, 136(3B): B864-B871.
[23]	KOHN W, SHAM L.Self-consistent equations including exchange and correlation effects.Phys. Rev., 1965, 140(4A): A1133-A1138.
[24]	OUYANG Y, ZHONG X.Interatomic potentials for computer simulation of condensed matters,Advances in Mechanics, 2006, 36(3): 321-343.
[25]	RAPAPORT D C.The Art of Molecular Dynamics Simulation, Second Edition. Cambridge: Cambridge University Press, 2004: 1-124.
[26]	CHEN L Q.Phase-field models for microstructure evolution.Annu. Rev. Mater. Res., 2002, 32(1): 113-140.
[27]	CHEN L Q, YANG W.Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain-growth kinetics.Phys. Rev. B, 1994, 50(21): 15752-15756.
[28]	FONG D D, STEPHENSON G B, STREIFFER S K, et al.Ferroelectricity in ultrathin perovskite films.Science, 2004, 304(5677): 1650-1653.
[29]	JUNQUERA J, GHOSEZ P.Critical thickness for ferroelectricity in perovskite ultrathin films.Nature, 2003, 422(6931): 506-509.
[30]	SAI N, KOLPAK A M, RAPPE A M. Ferroelectricity in ultrathin perovskite films. Phys. Rev. B, 2005, 72(2): 020101(R)-1-4.
[31]	UMENO Y, ALBINA J M, MEYER B, et al. Ab initio calculations of ferroelectric instability in PbTiO3 capacitors with symmetric and asymmetric electrode layers. Phys. Rev. B, 2009, 80(20): 205122-1-8.
[32]	AGUADO-PUENTA P, JUNQUERA J. Ferromagneticlike closure domains in ferroelectric ultrathin films: first-principles simulations. Phys. Rev. Lett., 2008, 100(17): 177601-1-4.
[33]	DREZNER Y, BERGER S.Thermodynamic stability of BaTiO3 nano-domains.Materials Letters, 2005, 59(12): 1598-1602.
[34]	TENNE D A, TURNER P, SCHMIDT J D, et al. Ferroelectricity in ultrathin BaTiO3 films: probing the size effect by ultraviolet Raman spectroscopy. Phys. Rev. Lett., 2009, 103(17): 177601-1-4.
[35]	YIN B, QU S. Origin of the vanishing critical thickness for ferroelectricity in free-standing PbTiO3 ultrathin films from first principles. J. Appl. Phys., 2013, 114(6): 063703-1-6.
[36]	RESTA R, POSTERNAK M, BALDERESCHI A.Towards a quantum theory of polarization in ferroelectrics: the case of KNbO3.Phys. Rev. Lett., 1993, 70(7): 1010-1013.
[37]	KING-SMITH R D, VANDERBILT D. First-principles investigation of ferroelectricity in perovskite compounds.Phys. Rev. B, 1994, 49(9): 5828-5844.
[38]	SHIRANE G, PEPINSKY R.X-ray and neutron diffraction study of ferroelectric PbTiO3.Acta Crystallographica, 1956, 9(2): 131-140.
[39]	GLAZER A M, MABUD S A.Powder profile refinement of lead zirconate titanate at several temperatures: II. Pure PbTiO3.Acta Crystallographica, Section B: Structural Science, 1978, 34(4): 1065-1070.
[40]	RESTA R.Manifestations of Berry’s phase in molecules and condensed matter.J. Phys.: Condens. Matter, 2000, 12(9): R107-R143.
[41]	RABE K M.Theoretical investigations of epitaxial strain effects in ferroelectric oxide thin films and superlattices.Current Opinion in Solid State and Materials Science, 2005, 9(3): 122-127.
[42]	FUJISAWA H, SHIMIZU M, NIU H, et al. Ferroelectricity and local currents in epitaxial 5 - and 9-nm-thick Pb (Zr, Ti)O3 ultrathin films by scanning probe microscopy. Appl. Phys. Lett., 2005, 86(1): 012903-1-3.
[43]	KOTOMIN E A, HEIFETS E, DORFMAN S, et al. Comparative study of polar perovskite surfaces. Surface Science, 2004, 566-568(1): 231-235.
[44]	LAI B K, KORNEV L A, BELLAICHE L, et al. Phase diagrams of epitaxial BaTiO3 ultrathin films from first principles. Appl. Phys. Lett., 2005, 86(13): 132904-1-3.
[45]	MUNKHOLM A, STREIFFER S K, RAMANA MURTY M V, et al. Antiferrodistortive reconstruction of the PbTiO3 (001) surface. Phys. Rev. Lett., 2001, 88(1): 0161010-1-4.
[46]	BUNGARO C, RABE K M. Coexistence of antiferrodistortive and ferroelectric distortions at the PbTiO3 (001) surface. Phys. Rev. B, 2005, 71(3): 035420-1-9.
[47]	KRETSCHMER R, BINDER K.Surface effects on phase transitions in ferroelectrics and dipolar magnets.Phys. Rev. B, 1979, 20(3): 1065-1076.
[48]	UMENO Y, SHIMADA T, KITAMURA T, et al. Ab initio density functional theory study of strain effects on ferroelectricity at PbTiO3 surfaces. Phys. Rev. B, 2006, 74(17): 174111-1-9.
[49]	BOUSQUET E, DAWBER M, STUCKI N, et al.Improper ferroelectricity in perovskite oxide artificial superlattices.Nature, 2008, 452(7188): 732-736.
[50]	MEYER B, PADILLA J, VANDERBILT D.Theory of PbTiO3, BaTiO3, and SrTiO3 surfaces.Faraday Discussion, 1999, 114: 395-405.
[51]	GU H, HU Y, YOU J, HU Z, et al. Characterization of singlecrystalline PbTiO3 nanowire growth via surfactant-free hydrothermal method. J. Appl. Phys., 2007, 101(2): 024319-1-7.
[52]	URBAN J J, YUN W S, GU Q, et al.Synthesis of single-crystalline perovskite nanorods composed of barium titanate and strontium titanate.J. Am. Chem. Soc., 2002, 124(7): 1186-1187.
[53]	YAMASHITA Y, MUKAI K, YOSHINOBU J, et al.Chemical nature of nanostructures of La0.6Sr0.4MnO3 on SrTiO3 (100).Surface Science, 2002, 514(1/2/3): 54-59.
[54]	CHO G B, YAMAMOTO M, ENDO Y. Surface features of self-organized SrTiO3 (001) substrates inclined in [100] and [110] directions. Thin Solid Films, 2004, 464-465: 80-84.
[55]	TAKAHASHI K, SUZUKI M, YOSHIMOTO M, et al.Growth behavior of c-axis-oriented epitaxial SrBi2Ta2O9 films on SrTiO3 substrates with atomic scale step structure.Jpn. J. Appl. Phys., 2006, 45(5): L138-L141.
[56]	CHU M W, SZAFRANIAK I, SCHOLZ R, et al.Impact of misfit dislocations on the polarization instability of epitaxial nanostructured ferroelectric perovskites.Nature Materials, 2004, 3(2): 87-90.
[57]	JEON J H, CHOI S K. Growth mode transition to pyramid from layer by layer of heteroepitaxial PbTiO3 islands on a (001) vicinal SrTiO3 substrate fabricated by hydrothermal epitaxy. Appl. Phys. Lett., 2007, 91(9): 091916-1-3.
[58]	SHIMADA T, TOMODA S, KITAMURA T. Ab initio study of ferroelectricity in edged PbTiO3 nanowires under axial tension. Phys. Rev. B, 2009, 79(2): 024102-1-7.
[59]	GENESTE G, BOUSQUET E, JUNQUERA J, et al. Finite-size effects in BaTiO3 nanowires. Appl. Phys. Lett., 2006, 88(11): 112906-1-3.
[60]	PROSANDEEV S, PONOMAREVA I. Controlling toroidal moment by means of an inhomogeneous static field: An ab initio study. Phys. Rev. Lett., 2006, 96(23): 237601-1-4.
[61]	PROSANDEEV S, PONOMAREVA I, NAUMOV I, et al. Original properties of dipole vortices in zero-dimensional ferrroelectrics. J. Phys.: Condens. Matter, 2008, 20(19): 193201-1-14.
[62]	SCHILLING A, BYRNE D, GATALAN G, et al.Domains in ferroelectric nanodots.Nano Letter, 2009, 9(9): 3359-3364.
[63]	STACHIOTTI M G, SEPLIARSKY M. Toroidal ferroelctricity in PbTiO3 nanoparticles. Phys. Rev. Lett., 2011, 106(13): 137601-1-4.
[64]	WANG X, TOMODA S, SHIMADA T, et al. Local suppression of ferroelectricity at PbTiO3 surface steps: a density functional theory study. J. Phys.: Condens. Matter, 2012, 24(4): 045903-1-8.
[65]	SHIMADA T, TOMODA S, KITAMURA T. Ab initio study of ferroelectric closure domains in ultrathin PbTiO3 films. Phys. Rev. B, 2010, 81(14): 144116-1-6.
[66]	PILANIA G, RAMPRASAD R. Complex polarization ordering in PbTiO3 nanowires: a first-principles computational study. Phys. Rev. B, 2010, 82(15): 155442-1-8.
[67]	PILANIA G, ALPAY S P, RAMPRASAD R. Ab initio study of ferroelectricity in BaTiO3 nanowires. Phys. Rev. B, 2009, 80(1): 014113-1-7.
[68]	FU H, BELLAICHE L. Ferroelectricity in barium titanate quantum dots and wires. Phys. Rev. Lett., 2003, 91(25): 257601-1-4.
[69]	ZHU X H, LIU Z G.Size effects in perovskite ferroelectric nanostructures: current progress and future perspectives.Journal of Advanced Dielectrics, 2011, 1(3): 289-301.
[70]	SHIN H J, CHOI J H, YANG H J, et al. Patterning of ferroelectric nanodot arrays using a silicon nitride shadow mask. Appl. Phys. Lett., 2005, 87(11): 113114-1-3.
[71]	ZHONG W L, WANG Y G, ZHANG P L, et al.Phenomenological study of the size effect on phase transitions in ferroelectric particles.Phys. Rev. B, 1994, 50(2): 698-703.
[72]	ZHONG W L, AI S T, JIANG B.Two critical size of barium titanate and lead titanate.Journal of Inorganic Materials, 2002, 17(5): 1009-1012.
[73]	MOROZOVSKA A N, ELISEEV E A, GLINCHUK M D. Ferroelectricity enhancement in confined nanorods: direct variational method. Phys. Rev. B, 2006, 73(21): 214106-1-13.
[74]	LIN S, LU T Q, JIN C Q, et al. Size effect on the dielectric properties of BaTiO3 nanoceramics in a modified Ginsburg-Landau-Devonshire thermodynamics theory. Phys. Rev. B, 2006, 74(13): 134115-1-5.
[75]	WANG C L, XIN Y, WANG X S, et al.Size effects of ferroelectric particles described by the transverse Ising models.Phys. Rev. B, 2000, 62(17): 11423-11427.
[76]	ERDEN E, SEMMELHACK H C, BOTTCHER R, et al.Study of the tetragonal-to-cubic phase transition in PbTiO3 nanopowders.J. Phys.: Condens. Matter, 2006, 18(15): 3861-3874.
[77]	POLKING M J, HAN M G, YOURDKHANI A, et al.Ferroelectric order in individual nanometer-scale crystals.Nature Materials, 2012, 11(8): 700-709.
[78]	SEDYKH P, MICHEL D, CHARNAYA E V, et al.Size effects in fine barium titanate particles.Ferroelectrics, 2010, 400(1): 135-143.
[79]	SMITH M B, PAGE K, SIEGRIST T, et al.Crystal structure and the paraelectric-to-ferroelectric phase transition of nanoscale BaTiO3.J. Am. Chem. Soc., 2008, 130(22): 6955-6963.
[80]	WANG X H, DENG X Y, WEN H. Phase transition and high dielectric constant of bulk dense nano-grain barium titanate ceramic. Appl. Phys. Lett., 2006, 89(16): 162902-1-3.
[81]	DENG X Y, LI D J, LI J B.Preparation of nanocrystalline BaTiO3 ceramics.Science in China Series E: Technological Sciences, 2009, 52(6): 1730-1734.
[82]	XIAO C J, JIN C Q, WANG X H.Crystal structure and ferroelectricity of nanocrystalline barium titanate ceramics fabricated by the high pressure sintering.Journal of the Chinese Ceramic Society, 2008, 36(6): 748-750.
[83]	MÜNCH I, HUBER J E. A hexadomain vortex in tetragonal ferroelectrics. Appl. Phys. Lett., 2009, 95(2): 022913-1-3.
[84]	ONG L, SOH A K, LIU S Y, et al. Vortex structure transformation of BaTiO3 nanoparticles through the gradient function. J. Appl. Phys., 2009, 106(2): 024111-1-4.