铁电薄膜的静态特性及动态介电特性的结构过渡层效应
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摘要
铁电薄膜与体材料相比可以具有良好的压电、热释电、电光、声光、光折变效应、非线性光学效应和高介电系数等优良特性[10]。近十几年来,铁电薄膜的制备技术有了很大的进步,极大地拓宽了应用领域的范围。例如非易失性铁电存储器(FERAM)、动态随机存储器(DRAM)、薄膜电容器、微驱动器和执行器、红外探测器、热释电传感器列阵、光波导器件、光学显示及存储器、空间光调制器、激光倍频器等。随着科技的日益发展和研究的深入,人们期望基于铁电薄膜的设备能够小型化、高密度和低能量损耗等等。然而,由于制备过程中杂质、缺陷、表面和界面应力以及不同组分间的界面效应等因素,导致铁电薄膜的物理性质与相应体材料的不同,有些情况下这种差别非常大。也会出现新的现象,如尺寸效应等。从众多已经发表的关于铁电薄膜制备和性质的研究报告中能够知道以下问题,所有研究结果均存在个体的差异,即使工艺相同、材料成分一样也是如此。这说明铁电薄膜的物理性质不但与材料和其成分有关,而且与具体工艺过程细节有关。通过调研和大量已发表的研究结果分析,我们认为由于铁电薄膜与电极之间、不同材料间的界面应力以及缺陷都是原生的,实验的个体差异就是原生的应力及缺陷分布不同所致,它们的存在会造成薄膜结构的局部差异,结果会在薄膜的表面或界面附近产生结构过渡区,正是这种结构过渡区对铁电薄膜性质的影响能够产生较大的影响,甚至可以导致体材料没有的物理效应。因而无论从是科学认识过程要求和理论发展的需求,还是为了制备高质量、工作稳定的更小尺寸的商业化器件都要求人们做进一步的基础实验和理论研究工作。因而对表面或界面过渡层效应的基础研究,不但具有理论研究意义而且具有非常实际的研究价值。本论文就是在这样的背景下,通过引入结构过渡层,研究铁电薄膜的静态性质和动态介电性质。
本文分别采用横场Ising模型、GLD唯象理论,在平均场近似下研究了铁电薄膜的极化分布、相变温度及热释电等性质的表面过渡层效应。
在采用横场Ising模型的理论研究中,首次引入了层内赝自旋相互作用函数J_a(m)和层间赝自旋相互作用函数J_a(m)来表征表面过渡层内的结构的不均匀特点。这是对推广使用横场Ising模型研究铁电薄膜的可能产生推动作用的主要创新之一。得到新结论有:(1)铁电薄膜存在表面过渡层是薄膜性质不同于体材料的本质原因,而过渡层厚度是影响铁电薄膜静态性质的一个很重要的因素。(2)表面过渡层可以使薄膜的相变温度高于或低于体材料的相变温度。在过渡层中层内赝自旋相互作用系数比层间赝自旋相互作用系数对于体系性质的影响要更加显著。(3)由于表面过渡层(赝自旋相互作用系数小于相应体材料的值情况)的作用,当赝自旋相互作用较弱时,薄膜存在临界的厚度,如果薄膜的厚度小于临界厚度时铁电薄膜的铁电性将消失。
为了探讨结构过渡层对铁电超晶格、多层铁电薄膜性质的影响,论文研究了对在界面附近存在结构过渡区和在界面处两组分存在铁电耦合的双层铁电薄膜的性质进行了理论探讨。在这种构型的铁电复合薄膜研究中,论文首次把结构过渡层引入研究中,为深入了解这种构型的铁电复合薄膜的奇异特性产生的物理机制提出了新的认识方向。为使结果具有普适性,采用了GLD唯象理论。得到以下主要结论是:在界面间界耦合为铁电耦合的情况下,界面间界耦合有利于薄膜处于铁电相,而结构过渡层对系统的铁电性有抑制作用。在这种构型的情况下,铁电双层膜将存在一个两种相互抵制作用的平衡点。铁电双层膜性质奇异的反常行为表现是源于结构过渡层和界面间耦合之间的竞争偏离平衡点。例如当体系处于界面间界耦合的作用小于结构过渡层时状态时,可能产生尺寸驱动的相变。反之,不能发生尺寸驱动的相变。
论文首次在平均场近似理论框架下,讨论表面结构过渡层对薄膜的动态介电常数的影响,得到如下结论:(1)晶格振动阻尼作用是降低相对介电常数实部和虚部的峰值,并且拓宽峰宽。(2)结构过渡层能使相对介电常数的实部和虚部的峰值的温度位置向低温区移动,软模频率将随着结构过渡层影响的增加而降低。
本论文是在热力学宏观理论和平均场近似理论的框架下,研究了铁电薄膜的静态性质和动态性质,以及铁电双层薄膜的极化分布和相变性质。所取得的结果和结论丰富了铁电薄膜领域的研究内容,对实验工作可能具有一定的指导作用。但是尚有许多工作有待进一步研究,例如:薄膜内部的退极化场问题等。
Ferroelectric thin films have various unique characteristics, such as piezoelectricity, pyroelectricity, electro-optic, acousto-optic, photorefractive effect, non-linear optics effect and high dielectric constant and so on, compared to the bulk materials. Within ten years, the application fields of ferroelectric thin films have been broadened because of the great advancement of prepared techniques. For example, nonvolatile memory, dynamic random memory, film capacitor, micro-driver and actuator, infrared detector, pyroelectric sensor array, fiber waveguide device, optic display and memory, spatial light modular, laser frequency booster, etc. With the developments of technology increasingly and studies deeply, a number of advantages are expected from ferroelectric thin film based devices: miniaturization, high density and low-power consumption. However, the physical properties of ferroelectric thin films are different from those of the corresponding bulk materials due to some factors, such as impurities, defects, surface and interfacial stress when films are prepared, as well as the interface effects between different components and so on. In some case, such distinction is great. The new phenomena may also appear, for instance, size effects. From lots of research reports on the preparation and properties of ferroelectric thin films, we can know that all the results have individual differences, even if the technology and material elements are the same. It is indicated that the characters of ferroelectric thin films associate not only the materials and elements, but also the details of technologic process. Based on the analysis of the reported results, we consider the interfacial stress between the ferroelectric thin films and electrodes and between the different materials, as well as the defects are protogenic. The individual differences in experiments are ascribed to the protogenic stress and different distribution of the defect, which can induce the local differences in film structure. Hence, the structure transition zone, which may exist at the surface or near the interface of the films, has a great impact on the properties of ferroelectric thin films. Even the physic effects, which cannot be in the bulk materials, can be induced. The basis of experimental and theoretical research is further requested, whether the need of science cognitive process and theoretical development, or preparation of smaller scale commercial devices with high quality and stability of work. Therefore, the basic study on the surface or interface effects has both theoretical significance and actual value. Under such background, the statical and dynamical properties of a ferroelectric thin film are investigated by introducing the structure transition layer.
Using the transverse Ising model and GLD phenomenological theory, respectively, the surface transition layer effects of the properties of the polarization distribution, transition temperature and pyroelectric, etc, are investigated within the framework of the mean field approximation.
Functions of the intra-layerJ_a(m) and inter-layerJ_a(m) coupling are introduced to characterize the nonuniform structure of surface transition layer based on the transverse Ising model theory for the first time. It is one of the primary innovations for generalizing the use of Ising model to study a ferroelectric thin film. The results obtained are: (1) the essential reason of the properties of ferroelectric thin films different from those of bulk materials is the existence of surface transition layer which is an important factor for influence of the static properties of ferroelectric thin films. (2) surface transition layer can make the transition temperature of ferroelectric thin films higher than that of bulk materials or lower. The influence of the intra-layer pseudo-spin interaction constant on the properties of the system is more obvious than that of the inter-layer. (3) due to the influence of the surface transition layer (pseudo-spin interaction coefficient is less than the value of bulk materials) , the critical thickness will exist in the films if the pseudo-spin interaction is weak; if the thickness of the films is less than the critical thickness, the ferroelectricity of ferroelectric thin films disappears.
For discussing the influence of structure transition layer on the properties of ferroelectric superlattice and multilayer thin films, the characteristics of ferroelectric bilayer films with the structure transition layer near interface and interfacial coupling between two components are discussed. The structure transition layer is introduced into a ferroelectric compound thin film firstly, and the way of the new cognition is provided for understanding the physical mechanism of abnormal characters of a ferroelectric compound thin film. Without the generality of the results, we use GLD phenomenological theory. The conclusions are: there may be an equilibrium point of the two contrary actions in the system, in the case of the interfacial coupling constant (ferroelectric coupling) advantage to the ferroelectric phase for the system and surface transition layer suppressed the system at ferroelectric phase. The abnormal behaviors of a ferroelectric bilayer film are ascribed to the competition between the surface transition layer and interfacial coupling deviated from the equilibrium point. For example, if the action of the interfacial coupling is dominant, the size-driven phase transition may occur, and the vice versa.
Influence of the surface transition layer on the dynamical dielectric constant is discussed first within the framework of the mean field approximation. The following results are: (1) the action of the lattice vibrato damp reduce the peak value of the real and imaginary parts of the permittivity, and broaden the width of the peak. (2) surface transition layer is responsible for the shift of the peaks of the real and imaginary parts of the permittivity to the lower temperature, and the frequency of the soft mode reduces with increasing the influence intensity of surface transition layers.
The statical and dynamical properties of a ferroelectric thin film and the polarization distribution and phase transition of a ferroelectric bilayer film have been investigated within the framework of the macroscopical thermodynamic theory and mean field approximation. The results and conclusions we obtained enrich the study contents of ferroelectric thin film fields, and may have some significance for experiments. However, a number of tasks are still further investigated, for example, the problem of depolarization field in the interior of films.
本文分别采用横场Ising模型、GLD唯象理论,在平均场近似下研究了铁电薄膜的极化分布、相变温度及热释电等性质的表面过渡层效应。
在采用横场Ising模型的理论研究中,首次引入了层内赝自旋相互作用函数J_a(m)和层间赝自旋相互作用函数J_a(m)来表征表面过渡层内的结构的不均匀特点。这是对推广使用横场Ising模型研究铁电薄膜的可能产生推动作用的主要创新之一。得到新结论有:(1)铁电薄膜存在表面过渡层是薄膜性质不同于体材料的本质原因,而过渡层厚度是影响铁电薄膜静态性质的一个很重要的因素。(2)表面过渡层可以使薄膜的相变温度高于或低于体材料的相变温度。在过渡层中层内赝自旋相互作用系数比层间赝自旋相互作用系数对于体系性质的影响要更加显著。(3)由于表面过渡层(赝自旋相互作用系数小于相应体材料的值情况)的作用,当赝自旋相互作用较弱时,薄膜存在临界的厚度,如果薄膜的厚度小于临界厚度时铁电薄膜的铁电性将消失。
为了探讨结构过渡层对铁电超晶格、多层铁电薄膜性质的影响,论文研究了对在界面附近存在结构过渡区和在界面处两组分存在铁电耦合的双层铁电薄膜的性质进行了理论探讨。在这种构型的铁电复合薄膜研究中,论文首次把结构过渡层引入研究中,为深入了解这种构型的铁电复合薄膜的奇异特性产生的物理机制提出了新的认识方向。为使结果具有普适性,采用了GLD唯象理论。得到以下主要结论是:在界面间界耦合为铁电耦合的情况下,界面间界耦合有利于薄膜处于铁电相,而结构过渡层对系统的铁电性有抑制作用。在这种构型的情况下,铁电双层膜将存在一个两种相互抵制作用的平衡点。铁电双层膜性质奇异的反常行为表现是源于结构过渡层和界面间耦合之间的竞争偏离平衡点。例如当体系处于界面间界耦合的作用小于结构过渡层时状态时,可能产生尺寸驱动的相变。反之,不能发生尺寸驱动的相变。
论文首次在平均场近似理论框架下,讨论表面结构过渡层对薄膜的动态介电常数的影响,得到如下结论:(1)晶格振动阻尼作用是降低相对介电常数实部和虚部的峰值,并且拓宽峰宽。(2)结构过渡层能使相对介电常数的实部和虚部的峰值的温度位置向低温区移动,软模频率将随着结构过渡层影响的增加而降低。
本论文是在热力学宏观理论和平均场近似理论的框架下,研究了铁电薄膜的静态性质和动态性质,以及铁电双层薄膜的极化分布和相变性质。所取得的结果和结论丰富了铁电薄膜领域的研究内容,对实验工作可能具有一定的指导作用。但是尚有许多工作有待进一步研究,例如:薄膜内部的退极化场问题等。
Ferroelectric thin films have various unique characteristics, such as piezoelectricity, pyroelectricity, electro-optic, acousto-optic, photorefractive effect, non-linear optics effect and high dielectric constant and so on, compared to the bulk materials. Within ten years, the application fields of ferroelectric thin films have been broadened because of the great advancement of prepared techniques. For example, nonvolatile memory, dynamic random memory, film capacitor, micro-driver and actuator, infrared detector, pyroelectric sensor array, fiber waveguide device, optic display and memory, spatial light modular, laser frequency booster, etc. With the developments of technology increasingly and studies deeply, a number of advantages are expected from ferroelectric thin film based devices: miniaturization, high density and low-power consumption. However, the physical properties of ferroelectric thin films are different from those of the corresponding bulk materials due to some factors, such as impurities, defects, surface and interfacial stress when films are prepared, as well as the interface effects between different components and so on. In some case, such distinction is great. The new phenomena may also appear, for instance, size effects. From lots of research reports on the preparation and properties of ferroelectric thin films, we can know that all the results have individual differences, even if the technology and material elements are the same. It is indicated that the characters of ferroelectric thin films associate not only the materials and elements, but also the details of technologic process. Based on the analysis of the reported results, we consider the interfacial stress between the ferroelectric thin films and electrodes and between the different materials, as well as the defects are protogenic. The individual differences in experiments are ascribed to the protogenic stress and different distribution of the defect, which can induce the local differences in film structure. Hence, the structure transition zone, which may exist at the surface or near the interface of the films, has a great impact on the properties of ferroelectric thin films. Even the physic effects, which cannot be in the bulk materials, can be induced. The basis of experimental and theoretical research is further requested, whether the need of science cognitive process and theoretical development, or preparation of smaller scale commercial devices with high quality and stability of work. Therefore, the basic study on the surface or interface effects has both theoretical significance and actual value. Under such background, the statical and dynamical properties of a ferroelectric thin film are investigated by introducing the structure transition layer.
Using the transverse Ising model and GLD phenomenological theory, respectively, the surface transition layer effects of the properties of the polarization distribution, transition temperature and pyroelectric, etc, are investigated within the framework of the mean field approximation.
Functions of the intra-layerJ_a(m) and inter-layerJ_a(m) coupling are introduced to characterize the nonuniform structure of surface transition layer based on the transverse Ising model theory for the first time. It is one of the primary innovations for generalizing the use of Ising model to study a ferroelectric thin film. The results obtained are: (1) the essential reason of the properties of ferroelectric thin films different from those of bulk materials is the existence of surface transition layer which is an important factor for influence of the static properties of ferroelectric thin films. (2) surface transition layer can make the transition temperature of ferroelectric thin films higher than that of bulk materials or lower. The influence of the intra-layer pseudo-spin interaction constant on the properties of the system is more obvious than that of the inter-layer. (3) due to the influence of the surface transition layer (pseudo-spin interaction coefficient is less than the value of bulk materials) , the critical thickness will exist in the films if the pseudo-spin interaction is weak; if the thickness of the films is less than the critical thickness, the ferroelectricity of ferroelectric thin films disappears.
For discussing the influence of structure transition layer on the properties of ferroelectric superlattice and multilayer thin films, the characteristics of ferroelectric bilayer films with the structure transition layer near interface and interfacial coupling between two components are discussed. The structure transition layer is introduced into a ferroelectric compound thin film firstly, and the way of the new cognition is provided for understanding the physical mechanism of abnormal characters of a ferroelectric compound thin film. Without the generality of the results, we use GLD phenomenological theory. The conclusions are: there may be an equilibrium point of the two contrary actions in the system, in the case of the interfacial coupling constant (ferroelectric coupling) advantage to the ferroelectric phase for the system and surface transition layer suppressed the system at ferroelectric phase. The abnormal behaviors of a ferroelectric bilayer film are ascribed to the competition between the surface transition layer and interfacial coupling deviated from the equilibrium point. For example, if the action of the interfacial coupling is dominant, the size-driven phase transition may occur, and the vice versa.
Influence of the surface transition layer on the dynamical dielectric constant is discussed first within the framework of the mean field approximation. The following results are: (1) the action of the lattice vibrato damp reduce the peak value of the real and imaginary parts of the permittivity, and broaden the width of the peak. (2) surface transition layer is responsible for the shift of the peaks of the real and imaginary parts of the permittivity to the lower temperature, and the frequency of the soft mode reduces with increasing the influence intensity of surface transition layers.
The statical and dynamical properties of a ferroelectric thin film and the polarization distribution and phase transition of a ferroelectric bilayer film have been investigated within the framework of the macroscopical thermodynamic theory and mean field approximation. The results and conclusions we obtained enrich the study contents of ferroelectric thin film fields, and may have some significance for experiments. However, a number of tasks are still further investigated, for example, the problem of depolarization field in the interior of films.
引文
1钟维烈.第一章绪论热释电效应《.铁电体物理学》.科学出版社. 2002: 7~8
2 G. Busch and P. Scherrer. A new seignetto-electric substance. Naturwiss. 1935, 23: 737~38
3 G. Busch. New seignetto electrics. Helv. Phys. Acta. 1939, 11: 169~172
4 G. A. Smolenski, V.A. Isupov, A.I. Agranovskaya and S.N. Popov. Ferroelectrics with diffuse phase transitions. Sov. Phys. Solid State. 1961, 2: 2584~2594
5 V.A. Bokov and I.E. Myinikova. Ferroelectric properties of monocrystals of new perovskite compounds. Sov. Phys. Solid State. 1961, 2: 2428~243
6 N. Sicron, B. Ravel, Y. Yacoby, E.A. Stern, F. Dogan and J.J. Rehr. Nature of the ferroelectric phase transition in PbTiO 3 . Phys. Rev. B. 1994, 50: 13168~13180
7干福熹.信息材料.天津大学出版社, 2000: 469~531
8朱冬生,赵朝晖.溶胶-凝胶法制备纳米薄膜的研究进展.材料导报. 2003, 17(专): 53~55
9 C.H. Yang, Z. Wang. Preparation and main characteristics of lead-free K_(0.5) Bi_(0.5) TiO_3 ferroelectric thin films. J. Cryst. Growth. 2004: 304~307
10 W. Gong and J.F. Li. Effect of pyrolysis temperature on preferential orientation and electrical properties of sol-gel derived lead zironate titanate films. J. Euro. Geramic Society. 2004, 24: 2977~2982
11 Z. J. Wei and S. Bo. Dielectric and ferroelectric properties of Ba(Sn_(0.15) Ti_(0.85))O_3 thin films grown by a sol-gel process. Materials Research Bulletin. 2004, 39: 1599~1606
12 N.V. Gridharan, S. Madeswaran and S. Jayavel. Structural morph -ology and electrical studies on ferroelectric bismuth titanate thin films prepared by sol-gel technique. J. Cryst. Growth. 2004,237-39 (1):468~472
13新野正之,平井教雄,渡边龙三.倾斜机能材料.日本复合材料学会志. 1987, 13: 257~264
14 S. Suresh. Graded materials for resistence to contact deformation and damage. Science. 2001,292: 2447~2451
15林晨,林化春,王国元,陈东,杨光义.纳米材料及其前景展望.青岛建筑工程学院学报. 2001, 22(4): 92~95
16黄旭涛,严密.功能梯度材料:回顾与展望.材料科学与工程. 1997,
15(4): 35~38
17陈逸清,郑元荣,林成鲁等.脉冲准分子激光PZT薄膜德制备.中国激光. 1994, 2(8): 631~634
18 L. Goux, M. Gervais, F. Gervais, C. Champeaux, A. Catherinot. Pulsed Laser Deposition of Ferroelectric BST Thin Films on Perovskite Substrates: an Infrared Characterization. The International Journal of Inorganic Materials. 2001, 3(7): 839~842
19钟维烈.第八章热释电效应.《铁电体物理学》.科学出版社.2002:534
20 M. Algueró, M. L. Calzada. L. Pardo. The Effect of Film Thickness on the Ferroelectric Properties of Sol-gel Prepared Lanthanum Modified Lead Titanate Thin Films. Journal of the European Ceramic Society. 1999, 19(7): 1481~1484
21黄龙波,李佐宜,卢德新等.溅射制备铁电薄膜及其性能测试德研究.人工晶体学报. 1994, 23(4): 291~295
22 I.Kanno,S.Hayashi,R.Takayama etal.Processing and Characteriza -tion of Ferroelectric Thin Films by Muti-ion-beam Sputtering. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. 1996, 112(1): 125~128
23 Kato K. Chemical routes for low-temperature processing of layer- structured perovskite thin films Integ.Ferroelec. 1998,22:13~22
24张柏顺,章天金.钛酸锶钡薄膜的制备及其光学特性的研究.电子元件与材料, 2004, 23(12): 1~3
25 Yang.C.H.,Park.S.S. and Yoon S.G. Characterization of ferro electricSrBi_2 Ta_2 O_9 thin films deposited by a radio-frequency magnetron sputtering technique. J. Integ.Ferroelec.1997,18:377
26 J.F.Scott, Ferroelectric memories today. Series. Ferroelectrics 2000,236:247~258
27 Sakashita,etal. Dependence of electrical properties on film thickness in Pb(Zr_x Ti_(1_x)O_3 thin films produced by metalorganic chemical vapor deposition . Appl.Phys.Lett.,1993,73:7857~7860
28 Eguchi.K.and Kigutoshi M. Chemical vapor deposition of (Ba,Sr)TiO_3 thin films for application in gigabit scale dynamic random access memories. Integ.Ferroelec. 1997,14:33~42
29 Pignolet A.etal. Epitaxial and large area PLD ferroelectric thin film heterostructures on silicon substrates. Integ.Ferroelec.1998,21: 485~498
30 Kazumi,Kato, Kiyotaka Tanaka , and Kazuyuki Suzuki , Phase transition in bottom-up BaTiO_3 films on Si. Appl. Phys. Lett. 2007,91: 172907
31 N. Ortega , Ashok Kumar , and R. S. Katiyar , Enhanced polarization and dielectric properties of Pb(Zr_(1_x) Ti_x )O-3 thin films. J. Appl. Phys. 2008,104: 074114~074118
32 L. Lian and N. R. Sottos , Effects of thickness on the piezoelectric and dielectric properties of lead zirconate titanate thin films, J. Appl. Phys. 2000, 87: 3941~3949
33 Yu.A.Boikov and T.claeson, Microstructure and dielectric parameters of epitaxial SrRuO_3 /BaTiO_3 /SrRuO_3 heterostructures. Appl. Phys. Lett. 2001, 89:5053~5055
34 S.X.Wang,M.S.Guo,etal. Low-loss tunable capacitors fabricated directly on gold bottom electrodes.Appl.Phys.Lett. 2006, 89: 212907 ~212910
35 Lee J.K., Song T.K. and Jung H.Y. Characterristic SrBi~ 2Ta~ 2O~ 9 thin films fabricated by the RF Magnetron sputtering technique. Integ. Ferroelec. 1997,15:115~125
36 Zhang DY, Huang DG, Li JH, Li K, Preparation and Electrical Properties of LiTa3O8 Thin Films. Journal of Inorganic Materials.2008,23: 1106~1110
37 M.Tyunina and J.Levoska, Polar state in epitaxial films of the relaxor ferroelectric PbMg_(1/3) Nb_(2/3) O_3 .Phys.Rev.B69,2004,224101.
38 W. Cochran. Crystal stability and the theory of ferroelectricity. Adv. Phys. 1960, 9: 387~423
39 Y. Watanabe. Theoretical stability of the polarization in a thin semiconducting ferroelectric. Phys. Rev. B. 1998, 57: 789~804
40 E. V. Charnaya, O.S. Pogorelova, and C. Tien. Phenomenological model for the antiferroelectric phase transition in thin films and small particles. Physica B. 2001, 305: 97~104
41 C.Zhou and D.M.Newns,Intrinsic dead layer effect and the perfor -mance of ferroelectric thin film capacitors. J.Appl.Phys. 1997,82: 3081~3086,
42 N.A.Pertsev,V.G.Koukhar,R.Waser and S.Hoffmann, Curie–Weiss -type law for the strain and stress effects on the dielectric response of ferroelectric thin films, Appl. Phys. Lett. 2000, 77 : 2596~2599
43 R. Kretschmer, K. Binder. Surface Effects on Phase Transitions in Ferroelectrics and Dipolar Magnets. Phys. Rev. B. 1979, 20(3-1): 1065~1076
44 W.L. Zhong, B.D. Qu, P.L. Zhang, and Y.G. wang. Thickness dependence of the dielectric suseceptibility of ferroelectric thin films. Phys.Rev.B. 1994, 50(17): 12375~12379
45 W.L.Zhong,B.D.Qu,P.L.Zhang and Y.G.Wang.Thickness dependen -ce of the dielectric susceptibility of ferroelectric thin films. Phys. Rev. B. 1994,50: 12375~12380
46 Zhiren Zhen and Tianquan Lü,“Influence of imperfect surface on properties of thin ferroelectric film, Phyaica B, 2003,334: 456~460
47 Tianquan Lüand Wenwu Cao,“Generalized continuum theory for ferroelectric thin film”, Phys.Rev. B 2002, 66: 024102-1~024102-5: 1~5
48 Tianquan Lü, Zhiren Zhen and Punan Sun,“Influence of interface between two ferro- electrics on a film on polarization distribution”, Phys. Stat. Sol. (b), 2003, 240: 255~258.
49 Shan Lin, Tianquan Lü,“Influence of imperfect surface on dielectric susceptibility in the ferroelectric thin film with second-order phase transition”, phys. stat. sol. (b) 2005,242(14): 2967~2975
50 Hui Chen, Tianquan Lu,Wenwu Cao.influence of imperfect surface layers on dielectric and pyroelectric properties of ferroelectric thin film.Physica B. 2006,373:177~179
51 Hui Chen, Tianquan Lü, Chuanwen Chen, Wenwu Cao. Theoretical studies on the pyroelectric properties of two component composite ferroelectric thin film. Phys. Lett. A, 2006, 360: 357~361.
52 Hui Chen, Tianquan Lü, Lian Cui, Wenwu Cao. Dielectric properties of ferroelectric thin films with surface transition layers. Physica A, 2008, 387: 1963~1971.
53 Shan Lin, Tianquan Lü, Wenwu Cao,“Theoretical study on the influenceof surface imperfections on the properties of ferroelectric thin films in first-order ferroelectric systems”, phys. stat. sol. (b) 2006, 243(12):2952~2961
54 Shan Lin, Tianquan Lü, Influence of imperfect surface on dielectric susceptibility in the ferroelectric thin film with second-order phase transition.Phys.stat.sol. (b). 2005, 242: 2967~2975
55 T.Lüand W.Cao.Influence of imperfect surface on properties of ferroelectric thin film .Microelectron.Eng. 2003,66: 818~824
56 P.G. de Gennes. Collective motion of hydrogen bonds. Solid State Commun. 1963, 1: 132~137
57 C.L. Wang, W.L. Zhong, and P.L. Zhang. The Curie temperature of ultra-thin ferroelectric films. J. Phys: Condens. Matter 1992, 4: 4743~4749
58 C.L. Wang, S.R.P. Smith, and D.R. Tilley. Ferroelectric thin films described by an Ising model in a transverse field. J. Phys: Condens. Matter 1994, 6: 9633~9646
59 C.L. Wang, Y.Xin, X.S. Wang, and W.L. Zhong. Size effects of ferroelectric particles described by the transverse Ising model. Phys. Rev. B. 2000, 62: 11423~11427
60 C.L. Wang, Z.K.Qin,D.L.Lin, First-order phase transition inorder-disorder ferroelectrics. Phys.Rev.B .1989, 40:680~685
61 P.F. Nie, Jian Zhang, Zhen Yin et al. Theoretical Study of Dielectric Susceptibility in Ferroelectric Thin Films. Phys. Lett. A. 2001, 290(3-4): 176~181
62 B.H. Teng and H.K.Sy. Green’s function investigation of transition properties of the transverse Ising model.Phys.Rev.B.2004,70: 104115~104119
63 B.H.Teng and H.K.Sy. Transition regions in the parameter space based on the transverse Ising model with a four-spin interaction. Europhys.Lett. 2005,72:823~829
64 J.M. Wesselinowa. On the theory of thin ferroelectric films. Phys. Stat. Sol.(b). 2001, 223: 737~743
65 J. M. Wesselinowa. Dielectric Susceptibility of Ferroelectric Thin Films. Solid State Commun. 2002,121(9-10): 489~492
66 J.M. Wesselinowa. Dynamical properties of thin ferroelectric films described by the transverse Ising model. Phys. Stat. Sol.(b). 2002, 231: 187~191
67 R. D. King-Smith and David Vanderbilt . First-principles investiga -tion of ferroelectricity in perovskite compounds .Phys.Rev.B, 1994,49:5828~5844
68 Ghose P.,Gonze X.,Michenaud J.P. .First-principles characterize -ation of the four phases of bariumtitanate. Ferroelectrics. 1999, 220:1~15
69 Y.X.Wang,W.L.zhong,etal.. First-principles study on the optical properties of NaNO_2 in the ferroelectric and paraelectric phase. Solid State Communications .2001,119:665~669
70 Y.X.Wang,W.L.zhong,et al..First-principles study on the optical properties of SrHfO_3 and SrTiO_3 . Sol.stat. commun. 2001, 120: 133~136
71 R.H.Cohen. Origin of ferroelectricity in perovskite oxides. Nature, 1992,358:136~138
72 R. D. King-Smith and David Vanderbilt . First-principles investigat–ion of ferroelectricity in perovskite compounds. Phys. Rev.B, 1994,49:5828~5844
73 A.W.Hewat.Cubic-tetragonal-orthorhombic-rhombohedral ferroele- ctric transitions in perovskite potassium niobate: neutron powder profile refinement of the structures. J.Phys.C:Solid State Phys.1973,6:2559~2572
74 H.J.Monkhorst,J.D.Pack.Special points for Brillouin-zone integra -tions. American Physical Society. Rev.B,1976,13:5188~5192
75 H.J.Bakker,S.Hunsche,H.Kurz. Quantum-mechanical description of the ferroelectric phase transition in LiTaO_3 . American Physical Society. Rev.B,1993, 48:9331~9335
76 Y.Tezuka,S.Shin,M.Ishigame. Hyper-Raman and Raman studies on the phase transition of ferroelectric LiTaO_3 . American Physical Society.rev.B,1994, 49:9312~9321
77 Soma Chattopadhyay, Pushan Ayyub, V.R.Palkar and Manu Multani. Size-induced diffuse phase transition in the nanocrystalline ferroelectric PbTiO_3 . Phys.Rev.B.1995, 52:13177~13183
78 E. V. Charnaya, O.S. Pogorelova, and C. Tien. Phenomenological model for the antiferroelectric phase transition in thin films and small particles. Physica B. 2001, 305: 97~104
79 E.K. Tan, J. Osman, and D.R. Tilley. Calculation of intrinsic hysteresis loops of ferroelectric thin films. Solid State Commun. 2001, 117: 59~64
80 B.D. Qu, W.L. Zhong, and P.L. Zhang. Phase-transition behavior of the spontaneous polarization and susceptibility of ferroelectric thin films. Phys. Rev. B. 1995, 52(2): 766~770
81 C.L. Wang, Y. Xin, X.S. Wang, W.L. Zhong and P.L. Zhang. Phase transition properties of ferroelectric superlattices with three later -native layers. Phys. Lett. A. 2000, 268: 117~122
82 X.G. Wang, S.H. Pan and G.Z. Yang. Phase transitions in Ising magnetic films and superlattices. Solid State Commun. 1999, 113: 59~62
83 C.L. Wang, W.L. Zhong and P.L. Zhang.The Curie temperature of ultra-thin ferroelectric films. J. Phys.: Condens. Matter. 1992, 3: 4743~4749
84 Benoit Guigues, Julie Guillan, Emmanuel Defa¨y, Pierre Garrec, DavidWolozan, Bernard Andr′e, Fr′ed′eric Laugier, Roland Pantel, Xavier Gagnard and Marc A¨?d . SrTiO_3 /BaTiO3 multilayers thin films for integrated tunable capacitors applications. Journal of the European Ceramic Society . 2007,27:3851~3854
85 M Dawber, C Lichtensteiger, M Cantoni, M Veithen, P Ghosez, K Johnston, K M Rabe and J M Triscone. Unusual Behavior of the Ferroelectric Polarization in PbTiO_3 /SrTiO_3 Superlattices. American Physical Society. 2005,95:177601~177605
86 J G Wu, D Q Xiao, J G Zhu, J L Zhu, J Z Tan and Q L Zhang. Enhanced dielectric and ferroelectric properties of Pb(Zr_(0.8) Ti_(0.2))O_3 /Pb(Zr_(0.2) Ti_(0.8))O_3 multilayered thin films prepared by Rf magnetron sputtering. Applied Physics Letters. 2007,90:08902~08905
87 V A Stephanovich, I A Lukyanchuk and M G Karkut. Domain–Enhanced Interlayer Coupling in Ferroelectric/Paraelectric Super -lattices. American Physical Society. 2005,94: 047601~047605
88 Ranjith, R. Nikhil, and S. B. Krupanidhi. Interfacial coupling and its size dependence in PbTiO3 and PbMg_(1/3) Nb_(2/3) O_3 multilayers. Phys.Rev.B. 2006,74:184104~184114
89 Zhao X Y, Liu S J, Zhu J H, Dai N and Hu G J. Ferroelectric and optical properties of Pb(Zr_x Ti_(1-x))O_3 bilayers. Chin. Phys. Lett. 2008, 57:5968~5972
90 Zhu Z Y, Wang H, Zheng Y and Li Q K. The first-principles study of ferroelectric behaviors of PbTiO_3 /SrTiO_3 and BaTiO_3 /SrTiO_3 superlattices. Chin. Phys. 2007, 16: 1780~1785
91 A L Roytburd, S Zhong and S P Alpay . Dielectric anomaly due to electrostatic coupling in ferroelectric-paraelectric bilayers and multilayers. Appl. Phys. Lett. 2005,87: 092902~092904
92 J Im, O Auciello and S K. Streiffer . Layered (Ba_x Sr_(1_x))Ti_(1+y) O_(3+z) thin films for high frequency tunable devices~(±1) . Thin Solid Films. 2002,413:243~247
93 D H Bao, S K Lee, X H Zhu, M Alexe and D Hesse. Growth,structure,and properties of all-epitaxial ferroelectric (Bi,La)_4 Ti_3 O_(12) /Pb(Zr_(0.4) Ti_(0.6))O_3 /(Bi,La)_4 Ti_3 O_(12) trilayered thin films on SrRuO_3 -covered SrTiO_3 (011) substrates. Appl. Phys. Lett. 2005, 86:082906~082909
94 Shimuta T, Nakagawara O, Makino T, Arai S, Tabata H and Kawai T. Enhancement of remanent polarization in epitaxial BaTiO_3 /SrTiO_3 superlattices with "asymmetric" structure . Journal of Applied Physics,2002 ,91:2290~2294
95 Bao D H, Zhu X H, Alexe M and Hesse D. Microstructure and ferroelectric properties of low-fatigue epitaxial, all (001)-oriented (Bi,La)_4 Ti_3 O_(12) /Pb(Zr_(0.4) Ti_(0.6))O_3 /(Bi,La)_4 Ti-3 O_(12) trilayered thin films on (001) SrTiO_3 substrates .J. Appl. Phys. 2005,98,014101:1
96 Jiagang Wu, Jiliang Zhu, Dingquan Xiao and Jianguo Zhu. Double hysteresis loop in (Pb_(0.90) La_(0.10))Ti 0.975 O 3 /Pb(Zr_(0.20) Ti_(0.80) )O_3 bilayer thin films . Appl. Phys. Lett. 2007,91:212905~212908
97 R Ranjith, R Nikhil and S B Krupanidhi. Interfacial coupling and its size dependence in PbTiO3 and PbMg 1/3 Nb_(2/3) O_3 multilayers. Phys. Rev. B.2006,74:184104~184114
98 D Qu, W L Zhong and R H Prince. Interfacial coupling in ferroelectric superlattices . Phys. Rev. B.1997, 55: 11218~11224
99 K H Chew, L H Ong, J Osman and D R Tilley. Hysteresis loops of ferroelectric bilayers and superlattices. Appl. Phys.Lett. 2000,77: 2755~2757
100 J B Neaton and K M Rabe. Theory of polarization enhancement in epitaxial BaTiO_3 /SrTiO_3 superlattices. Appl. Phys. Lett. 2003,82: 1586~1588
101 B Yang, D M Zhang, C D.Zheng, J Wang and J Yu. Hysteresis loops of first-order ferroelectric bilayers or superlattices and their size effect. J. Phys. 2007,40:5696~5702
102 NaohikoYasuda,HiroakiInaba,and HidehiroOhwa. Dielectric relaxationin the Pb(Yb_(1/2) Nb_(1/2))O_3 -PbTiO_3 solid solution single crystal near the morphotropic phase boundary . Appl.Phys.Lett. 2003,83:1409~1410
103 A. E. Glazounov, A. K. Tagantsev. Evidence for domain-type dynamics in the ergodic phase of the PbMg_(1/3) Nb_(2/3) O_3 relaxor ferroelectric. A. J. Bell, Phys. Rev. B. 1996: 53:11281~11284
104 M. Tyunina and J. Levoska. Effect of ac field on the dielectric behavior in epitaxial films of relaxor ferroelectric PbMg_(1/3) Nb_(2/3) O_3 . Phys. Rev. B. 2005,72:104112~104121
105 M. Tyunina and J. Levoska. Coexistence of ferroelectric and relaxor properties in epitaxial films of Ba_(1_x) Sr_x TiO_3 .Phys. Rev. B. 2004,70:132105~132109
106 Abdelilh Mejdoubi and Christian Brosseau. Intrinsic resonant behavior of metamaterials by finite element calculations. Phys. Rev. B. 2006, 74:165424~165429
107 A. Mejdoubi and Christian Brosseau. Duality and similarity proper -ties of the effective permittivity of two-dimensional hetero -geneous medium with inclusion of fractal geometry. Phys. Rev. E. 2006,73:031405~031413
108 A. Mejdoubi and Christian Brosseau. Finite-difference time -domain simulation of heterostructures with inclusion of arbitrarily complex geometry. J. Appl. Phys. 2006,99:063502~063508
109 Christian Brosseau and A. Beroual. Computational electro -magnetics and the rational design of new dielectric hetero -structures. Progress in Materials Science . 2003,48:373~456
110 V. Myroshnychenko and C. Brosseau. Finite-element method for calculation of the effective permittivity of random inhomogeneous media. Phys. Rev. B. 2005, 71:016701~016717
111 Ang, Z. Yu, R. Guo, and A. Bhalla. Calculation of dielectric constant and loss of two-phase composites. J. Appl. Phys. 2003, 93:3475~3480
112 Ohno, D. Suzuki, K. Ishikawa, M. Horiuchi, T. Matsuda, and H. Suzuki, Size effect for Ba(ZrxTix)O3 (x=0.05) nano-particles. Ferroelectrics. 2006, 337:25~32
113 S.Aubry, J. Dielectric relaxation in the Pb(Yb1/2Nb1/2)O3-PbTiO3 solid solution single crystal . Chem. Phys. 1975, 62: 3216~3222
2 G. Busch and P. Scherrer. A new seignetto-electric substance. Naturwiss. 1935, 23: 737~38
3 G. Busch. New seignetto electrics. Helv. Phys. Acta. 1939, 11: 169~172
4 G. A. Smolenski, V.A. Isupov, A.I. Agranovskaya and S.N. Popov. Ferroelectrics with diffuse phase transitions. Sov. Phys. Solid State. 1961, 2: 2584~2594
5 V.A. Bokov and I.E. Myinikova. Ferroelectric properties of monocrystals of new perovskite compounds. Sov. Phys. Solid State. 1961, 2: 2428~243
6 N. Sicron, B. Ravel, Y. Yacoby, E.A. Stern, F. Dogan and J.J. Rehr. Nature of the ferroelectric phase transition in PbTiO 3 . Phys. Rev. B. 1994, 50: 13168~13180
7干福熹.信息材料.天津大学出版社, 2000: 469~531
8朱冬生,赵朝晖.溶胶-凝胶法制备纳米薄膜的研究进展.材料导报. 2003, 17(专): 53~55
9 C.H. Yang, Z. Wang. Preparation and main characteristics of lead-free K_(0.5) Bi_(0.5) TiO_3 ferroelectric thin films. J. Cryst. Growth. 2004: 304~307
10 W. Gong and J.F. Li. Effect of pyrolysis temperature on preferential orientation and electrical properties of sol-gel derived lead zironate titanate films. J. Euro. Geramic Society. 2004, 24: 2977~2982
11 Z. J. Wei and S. Bo. Dielectric and ferroelectric properties of Ba(Sn_(0.15) Ti_(0.85))O_3 thin films grown by a sol-gel process. Materials Research Bulletin. 2004, 39: 1599~1606
12 N.V. Gridharan, S. Madeswaran and S. Jayavel. Structural morph -ology and electrical studies on ferroelectric bismuth titanate thin films prepared by sol-gel technique. J. Cryst. Growth. 2004,237-39 (1):468~472
13新野正之,平井教雄,渡边龙三.倾斜机能材料.日本复合材料学会志. 1987, 13: 257~264
14 S. Suresh. Graded materials for resistence to contact deformation and damage. Science. 2001,292: 2447~2451
15林晨,林化春,王国元,陈东,杨光义.纳米材料及其前景展望.青岛建筑工程学院学报. 2001, 22(4): 92~95
16黄旭涛,严密.功能梯度材料:回顾与展望.材料科学与工程. 1997,
15(4): 35~38
17陈逸清,郑元荣,林成鲁等.脉冲准分子激光PZT薄膜德制备.中国激光. 1994, 2(8): 631~634
18 L. Goux, M. Gervais, F. Gervais, C. Champeaux, A. Catherinot. Pulsed Laser Deposition of Ferroelectric BST Thin Films on Perovskite Substrates: an Infrared Characterization. The International Journal of Inorganic Materials. 2001, 3(7): 839~842
19钟维烈.第八章热释电效应.《铁电体物理学》.科学出版社.2002:534
20 M. Algueró, M. L. Calzada. L. Pardo. The Effect of Film Thickness on the Ferroelectric Properties of Sol-gel Prepared Lanthanum Modified Lead Titanate Thin Films. Journal of the European Ceramic Society. 1999, 19(7): 1481~1484
21黄龙波,李佐宜,卢德新等.溅射制备铁电薄膜及其性能测试德研究.人工晶体学报. 1994, 23(4): 291~295
22 I.Kanno,S.Hayashi,R.Takayama etal.Processing and Characteriza -tion of Ferroelectric Thin Films by Muti-ion-beam Sputtering. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms. 1996, 112(1): 125~128
23 Kato K. Chemical routes for low-temperature processing of layer- structured perovskite thin films Integ.Ferroelec. 1998,22:13~22
24张柏顺,章天金.钛酸锶钡薄膜的制备及其光学特性的研究.电子元件与材料, 2004, 23(12): 1~3
25 Yang.C.H.,Park.S.S. and Yoon S.G. Characterization of ferro electricSrBi_2 Ta_2 O_9 thin films deposited by a radio-frequency magnetron sputtering technique. J. Integ.Ferroelec.1997,18:377
26 J.F.Scott, Ferroelectric memories today. Series. Ferroelectrics 2000,236:247~258
27 Sakashita,etal. Dependence of electrical properties on film thickness in Pb(Zr_x Ti_(1_x)O_3 thin films produced by metalorganic chemical vapor deposition . Appl.Phys.Lett.,1993,73:7857~7860
28 Eguchi.K.and Kigutoshi M. Chemical vapor deposition of (Ba,Sr)TiO_3 thin films for application in gigabit scale dynamic random access memories. Integ.Ferroelec. 1997,14:33~42
29 Pignolet A.etal. Epitaxial and large area PLD ferroelectric thin film heterostructures on silicon substrates. Integ.Ferroelec.1998,21: 485~498
30 Kazumi,Kato, Kiyotaka Tanaka , and Kazuyuki Suzuki , Phase transition in bottom-up BaTiO_3 films on Si. Appl. Phys. Lett. 2007,91: 172907
31 N. Ortega , Ashok Kumar , and R. S. Katiyar , Enhanced polarization and dielectric properties of Pb(Zr_(1_x) Ti_x )O-3 thin films. J. Appl. Phys. 2008,104: 074114~074118
32 L. Lian and N. R. Sottos , Effects of thickness on the piezoelectric and dielectric properties of lead zirconate titanate thin films, J. Appl. Phys. 2000, 87: 3941~3949
33 Yu.A.Boikov and T.claeson, Microstructure and dielectric parameters of epitaxial SrRuO_3 /BaTiO_3 /SrRuO_3 heterostructures. Appl. Phys. Lett. 2001, 89:5053~5055
34 S.X.Wang,M.S.Guo,etal. Low-loss tunable capacitors fabricated directly on gold bottom electrodes.Appl.Phys.Lett. 2006, 89: 212907 ~212910
35 Lee J.K., Song T.K. and Jung H.Y. Characterristic SrBi~ 2Ta~ 2O~ 9 thin films fabricated by the RF Magnetron sputtering technique. Integ. Ferroelec. 1997,15:115~125
36 Zhang DY, Huang DG, Li JH, Li K, Preparation and Electrical Properties of LiTa3O8 Thin Films. Journal of Inorganic Materials.2008,23: 1106~1110
37 M.Tyunina and J.Levoska, Polar state in epitaxial films of the relaxor ferroelectric PbMg_(1/3) Nb_(2/3) O_3 .Phys.Rev.B69,2004,224101.
38 W. Cochran. Crystal stability and the theory of ferroelectricity. Adv. Phys. 1960, 9: 387~423
39 Y. Watanabe. Theoretical stability of the polarization in a thin semiconducting ferroelectric. Phys. Rev. B. 1998, 57: 789~804
40 E. V. Charnaya, O.S. Pogorelova, and C. Tien. Phenomenological model for the antiferroelectric phase transition in thin films and small particles. Physica B. 2001, 305: 97~104
41 C.Zhou and D.M.Newns,Intrinsic dead layer effect and the perfor -mance of ferroelectric thin film capacitors. J.Appl.Phys. 1997,82: 3081~3086,
42 N.A.Pertsev,V.G.Koukhar,R.Waser and S.Hoffmann, Curie–Weiss -type law for the strain and stress effects on the dielectric response of ferroelectric thin films, Appl. Phys. Lett. 2000, 77 : 2596~2599
43 R. Kretschmer, K. Binder. Surface Effects on Phase Transitions in Ferroelectrics and Dipolar Magnets. Phys. Rev. B. 1979, 20(3-1): 1065~1076
44 W.L. Zhong, B.D. Qu, P.L. Zhang, and Y.G. wang. Thickness dependence of the dielectric suseceptibility of ferroelectric thin films. Phys.Rev.B. 1994, 50(17): 12375~12379
45 W.L.Zhong,B.D.Qu,P.L.Zhang and Y.G.Wang.Thickness dependen -ce of the dielectric susceptibility of ferroelectric thin films. Phys. Rev. B. 1994,50: 12375~12380
46 Zhiren Zhen and Tianquan Lü,“Influence of imperfect surface on properties of thin ferroelectric film, Phyaica B, 2003,334: 456~460
47 Tianquan Lüand Wenwu Cao,“Generalized continuum theory for ferroelectric thin film”, Phys.Rev. B 2002, 66: 024102-1~024102-5: 1~5
48 Tianquan Lü, Zhiren Zhen and Punan Sun,“Influence of interface between two ferro- electrics on a film on polarization distribution”, Phys. Stat. Sol. (b), 2003, 240: 255~258.
49 Shan Lin, Tianquan Lü,“Influence of imperfect surface on dielectric susceptibility in the ferroelectric thin film with second-order phase transition”, phys. stat. sol. (b) 2005,242(14): 2967~2975
50 Hui Chen, Tianquan Lu,Wenwu Cao.influence of imperfect surface layers on dielectric and pyroelectric properties of ferroelectric thin film.Physica B. 2006,373:177~179
51 Hui Chen, Tianquan Lü, Chuanwen Chen, Wenwu Cao. Theoretical studies on the pyroelectric properties of two component composite ferroelectric thin film. Phys. Lett. A, 2006, 360: 357~361.
52 Hui Chen, Tianquan Lü, Lian Cui, Wenwu Cao. Dielectric properties of ferroelectric thin films with surface transition layers. Physica A, 2008, 387: 1963~1971.
53 Shan Lin, Tianquan Lü, Wenwu Cao,“Theoretical study on the influenceof surface imperfections on the properties of ferroelectric thin films in first-order ferroelectric systems”, phys. stat. sol. (b) 2006, 243(12):2952~2961
54 Shan Lin, Tianquan Lü, Influence of imperfect surface on dielectric susceptibility in the ferroelectric thin film with second-order phase transition.Phys.stat.sol. (b). 2005, 242: 2967~2975
55 T.Lüand W.Cao.Influence of imperfect surface on properties of ferroelectric thin film .Microelectron.Eng. 2003,66: 818~824
56 P.G. de Gennes. Collective motion of hydrogen bonds. Solid State Commun. 1963, 1: 132~137
57 C.L. Wang, W.L. Zhong, and P.L. Zhang. The Curie temperature of ultra-thin ferroelectric films. J. Phys: Condens. Matter 1992, 4: 4743~4749
58 C.L. Wang, S.R.P. Smith, and D.R. Tilley. Ferroelectric thin films described by an Ising model in a transverse field. J. Phys: Condens. Matter 1994, 6: 9633~9646
59 C.L. Wang, Y.Xin, X.S. Wang, and W.L. Zhong. Size effects of ferroelectric particles described by the transverse Ising model. Phys. Rev. B. 2000, 62: 11423~11427
60 C.L. Wang, Z.K.Qin,D.L.Lin, First-order phase transition inorder-disorder ferroelectrics. Phys.Rev.B .1989, 40:680~685
61 P.F. Nie, Jian Zhang, Zhen Yin et al. Theoretical Study of Dielectric Susceptibility in Ferroelectric Thin Films. Phys. Lett. A. 2001, 290(3-4): 176~181
62 B.H. Teng and H.K.Sy. Green’s function investigation of transition properties of the transverse Ising model.Phys.Rev.B.2004,70: 104115~104119
63 B.H.Teng and H.K.Sy. Transition regions in the parameter space based on the transverse Ising model with a four-spin interaction. Europhys.Lett. 2005,72:823~829
64 J.M. Wesselinowa. On the theory of thin ferroelectric films. Phys. Stat. Sol.(b). 2001, 223: 737~743
65 J. M. Wesselinowa. Dielectric Susceptibility of Ferroelectric Thin Films. Solid State Commun. 2002,121(9-10): 489~492
66 J.M. Wesselinowa. Dynamical properties of thin ferroelectric films described by the transverse Ising model. Phys. Stat. Sol.(b). 2002, 231: 187~191
67 R. D. King-Smith and David Vanderbilt . First-principles investiga -tion of ferroelectricity in perovskite compounds .Phys.Rev.B, 1994,49:5828~5844
68 Ghose P.,Gonze X.,Michenaud J.P. .First-principles characterize -ation of the four phases of bariumtitanate. Ferroelectrics. 1999, 220:1~15
69 Y.X.Wang,W.L.zhong,etal.. First-principles study on the optical properties of NaNO_2 in the ferroelectric and paraelectric phase. Solid State Communications .2001,119:665~669
70 Y.X.Wang,W.L.zhong,et al..First-principles study on the optical properties of SrHfO_3 and SrTiO_3 . Sol.stat. commun. 2001, 120: 133~136
71 R.H.Cohen. Origin of ferroelectricity in perovskite oxides. Nature, 1992,358:136~138
72 R. D. King-Smith and David Vanderbilt . First-principles investigat–ion of ferroelectricity in perovskite compounds. Phys. Rev.B, 1994,49:5828~5844
73 A.W.Hewat.Cubic-tetragonal-orthorhombic-rhombohedral ferroele- ctric transitions in perovskite potassium niobate: neutron powder profile refinement of the structures. J.Phys.C:Solid State Phys.1973,6:2559~2572
74 H.J.Monkhorst,J.D.Pack.Special points for Brillouin-zone integra -tions. American Physical Society. Rev.B,1976,13:5188~5192
75 H.J.Bakker,S.Hunsche,H.Kurz. Quantum-mechanical description of the ferroelectric phase transition in LiTaO_3 . American Physical Society. Rev.B,1993, 48:9331~9335
76 Y.Tezuka,S.Shin,M.Ishigame. Hyper-Raman and Raman studies on the phase transition of ferroelectric LiTaO_3 . American Physical Society.rev.B,1994, 49:9312~9321
77 Soma Chattopadhyay, Pushan Ayyub, V.R.Palkar and Manu Multani. Size-induced diffuse phase transition in the nanocrystalline ferroelectric PbTiO_3 . Phys.Rev.B.1995, 52:13177~13183
78 E. V. Charnaya, O.S. Pogorelova, and C. Tien. Phenomenological model for the antiferroelectric phase transition in thin films and small particles. Physica B. 2001, 305: 97~104
79 E.K. Tan, J. Osman, and D.R. Tilley. Calculation of intrinsic hysteresis loops of ferroelectric thin films. Solid State Commun. 2001, 117: 59~64
80 B.D. Qu, W.L. Zhong, and P.L. Zhang. Phase-transition behavior of the spontaneous polarization and susceptibility of ferroelectric thin films. Phys. Rev. B. 1995, 52(2): 766~770
81 C.L. Wang, Y. Xin, X.S. Wang, W.L. Zhong and P.L. Zhang. Phase transition properties of ferroelectric superlattices with three later -native layers. Phys. Lett. A. 2000, 268: 117~122
82 X.G. Wang, S.H. Pan and G.Z. Yang. Phase transitions in Ising magnetic films and superlattices. Solid State Commun. 1999, 113: 59~62
83 C.L. Wang, W.L. Zhong and P.L. Zhang.The Curie temperature of ultra-thin ferroelectric films. J. Phys.: Condens. Matter. 1992, 3: 4743~4749
84 Benoit Guigues, Julie Guillan, Emmanuel Defa¨y, Pierre Garrec, DavidWolozan, Bernard Andr′e, Fr′ed′eric Laugier, Roland Pantel, Xavier Gagnard and Marc A¨?d . SrTiO_3 /BaTiO3 multilayers thin films for integrated tunable capacitors applications. Journal of the European Ceramic Society . 2007,27:3851~3854
85 M Dawber, C Lichtensteiger, M Cantoni, M Veithen, P Ghosez, K Johnston, K M Rabe and J M Triscone. Unusual Behavior of the Ferroelectric Polarization in PbTiO_3 /SrTiO_3 Superlattices. American Physical Society. 2005,95:177601~177605
86 J G Wu, D Q Xiao, J G Zhu, J L Zhu, J Z Tan and Q L Zhang. Enhanced dielectric and ferroelectric properties of Pb(Zr_(0.8) Ti_(0.2))O_3 /Pb(Zr_(0.2) Ti_(0.8))O_3 multilayered thin films prepared by Rf magnetron sputtering. Applied Physics Letters. 2007,90:08902~08905
87 V A Stephanovich, I A Lukyanchuk and M G Karkut. Domain–Enhanced Interlayer Coupling in Ferroelectric/Paraelectric Super -lattices. American Physical Society. 2005,94: 047601~047605
88 Ranjith, R. Nikhil, and S. B. Krupanidhi. Interfacial coupling and its size dependence in PbTiO3 and PbMg_(1/3) Nb_(2/3) O_3 multilayers. Phys.Rev.B. 2006,74:184104~184114
89 Zhao X Y, Liu S J, Zhu J H, Dai N and Hu G J. Ferroelectric and optical properties of Pb(Zr_x Ti_(1-x))O_3 bilayers. Chin. Phys. Lett. 2008, 57:5968~5972
90 Zhu Z Y, Wang H, Zheng Y and Li Q K. The first-principles study of ferroelectric behaviors of PbTiO_3 /SrTiO_3 and BaTiO_3 /SrTiO_3 superlattices. Chin. Phys. 2007, 16: 1780~1785
91 A L Roytburd, S Zhong and S P Alpay . Dielectric anomaly due to electrostatic coupling in ferroelectric-paraelectric bilayers and multilayers. Appl. Phys. Lett. 2005,87: 092902~092904
92 J Im, O Auciello and S K. Streiffer . Layered (Ba_x Sr_(1_x))Ti_(1+y) O_(3+z) thin films for high frequency tunable devices~(±1) . Thin Solid Films. 2002,413:243~247
93 D H Bao, S K Lee, X H Zhu, M Alexe and D Hesse. Growth,structure,and properties of all-epitaxial ferroelectric (Bi,La)_4 Ti_3 O_(12) /Pb(Zr_(0.4) Ti_(0.6))O_3 /(Bi,La)_4 Ti_3 O_(12) trilayered thin films on SrRuO_3 -covered SrTiO_3 (011) substrates. Appl. Phys. Lett. 2005, 86:082906~082909
94 Shimuta T, Nakagawara O, Makino T, Arai S, Tabata H and Kawai T. Enhancement of remanent polarization in epitaxial BaTiO_3 /SrTiO_3 superlattices with "asymmetric" structure . Journal of Applied Physics,2002 ,91:2290~2294
95 Bao D H, Zhu X H, Alexe M and Hesse D. Microstructure and ferroelectric properties of low-fatigue epitaxial, all (001)-oriented (Bi,La)_4 Ti_3 O_(12) /Pb(Zr_(0.4) Ti_(0.6))O_3 /(Bi,La)_4 Ti-3 O_(12) trilayered thin films on (001) SrTiO_3 substrates .J. Appl. Phys. 2005,98,014101:1
96 Jiagang Wu, Jiliang Zhu, Dingquan Xiao and Jianguo Zhu. Double hysteresis loop in (Pb_(0.90) La_(0.10))Ti 0.975 O 3 /Pb(Zr_(0.20) Ti_(0.80) )O_3 bilayer thin films . Appl. Phys. Lett. 2007,91:212905~212908
97 R Ranjith, R Nikhil and S B Krupanidhi. Interfacial coupling and its size dependence in PbTiO3 and PbMg 1/3 Nb_(2/3) O_3 multilayers. Phys. Rev. B.2006,74:184104~184114
98 D Qu, W L Zhong and R H Prince. Interfacial coupling in ferroelectric superlattices . Phys. Rev. B.1997, 55: 11218~11224
99 K H Chew, L H Ong, J Osman and D R Tilley. Hysteresis loops of ferroelectric bilayers and superlattices. Appl. Phys.Lett. 2000,77: 2755~2757
100 J B Neaton and K M Rabe. Theory of polarization enhancement in epitaxial BaTiO_3 /SrTiO_3 superlattices. Appl. Phys. Lett. 2003,82: 1586~1588
101 B Yang, D M Zhang, C D.Zheng, J Wang and J Yu. Hysteresis loops of first-order ferroelectric bilayers or superlattices and their size effect. J. Phys. 2007,40:5696~5702
102 NaohikoYasuda,HiroakiInaba,and HidehiroOhwa. Dielectric relaxationin the Pb(Yb_(1/2) Nb_(1/2))O_3 -PbTiO_3 solid solution single crystal near the morphotropic phase boundary . Appl.Phys.Lett. 2003,83:1409~1410
103 A. E. Glazounov, A. K. Tagantsev. Evidence for domain-type dynamics in the ergodic phase of the PbMg_(1/3) Nb_(2/3) O_3 relaxor ferroelectric. A. J. Bell, Phys. Rev. B. 1996: 53:11281~11284
104 M. Tyunina and J. Levoska. Effect of ac field on the dielectric behavior in epitaxial films of relaxor ferroelectric PbMg_(1/3) Nb_(2/3) O_3 . Phys. Rev. B. 2005,72:104112~104121
105 M. Tyunina and J. Levoska. Coexistence of ferroelectric and relaxor properties in epitaxial films of Ba_(1_x) Sr_x TiO_3 .Phys. Rev. B. 2004,70:132105~132109
106 Abdelilh Mejdoubi and Christian Brosseau. Intrinsic resonant behavior of metamaterials by finite element calculations. Phys. Rev. B. 2006, 74:165424~165429
107 A. Mejdoubi and Christian Brosseau. Duality and similarity proper -ties of the effective permittivity of two-dimensional hetero -geneous medium with inclusion of fractal geometry. Phys. Rev. E. 2006,73:031405~031413
108 A. Mejdoubi and Christian Brosseau. Finite-difference time -domain simulation of heterostructures with inclusion of arbitrarily complex geometry. J. Appl. Phys. 2006,99:063502~063508
109 Christian Brosseau and A. Beroual. Computational electro -magnetics and the rational design of new dielectric hetero -structures. Progress in Materials Science . 2003,48:373~456
110 V. Myroshnychenko and C. Brosseau. Finite-element method for calculation of the effective permittivity of random inhomogeneous media. Phys. Rev. B. 2005, 71:016701~016717
111 Ang, Z. Yu, R. Guo, and A. Bhalla. Calculation of dielectric constant and loss of two-phase composites. J. Appl. Phys. 2003, 93:3475~3480
112 Ohno, D. Suzuki, K. Ishikawa, M. Horiuchi, T. Matsuda, and H. Suzuki, Size effect for Ba(ZrxTix)O3 (x=0.05) nano-particles. Ferroelectrics. 2006, 337:25~32
113 S.Aubry, J. Dielectric relaxation in the Pb(Yb1/2Nb1/2)O3-PbTiO3 solid solution single crystal . Chem. Phys. 1975, 62: 3216~3222