钙钛矿型铁电薄膜材料具有铁电性、热电性、光电性、光折变性等多种性能，被越来越多的应用于微电子领域，成为制作非易失存储器、场效应管和热电传感器等的主要材料。但铁电薄膜厚度一般在微米以下，此时薄膜的尺寸效应很强，研究铁电薄膜材料的尺寸效应具有实际的理论和应用意义。 本文基于金茨堡-朗道-德文希尔（GLD）唯象理论框架，利用等效应变模型考虑薄膜内应变松弛，同时还结合薄膜表面晶格变化引起的极化改变和表面电荷引起的退极化效应等机电耦合边界条件，应用相场法建立了金茨堡-朗道-德文希尔时间发展方程。通过线性假设分析求解了顺电相向铁电相转变初始阶段居里温度随薄膜厚度的变化，并通过有限差分法数值求解了铁电薄膜...Ferroelectric thin films have been considerable importance in nonvolatile memory, field effect transistor, thermoelectric transducer and so on due to the ferroelectricity, thermoelectricity, photoelectricity and photorefractive properties. Generally, size effect is strong as the thickness of the films is always on nanoscale. So the investigations in this filed are significant. Basing on the Ginzb...学位：工学硕士院系专业：建筑与土木工程学院土木工程系_力学学号：2532008115179

张春祖

Xiamen University Institutional Repository

学校编码：10384                                 分类号      密级      学号：25320081151797                                        UDC             硕  士  学  位  论  文                                            应变松弛下铁电薄膜尺寸效应的相场模拟 Phase Field Modeling the Size Effect of Ferroelectric Thin Films by Considering the Relaxation of the Strain   张春祖  指导教师姓名：周志东 副教授 专  业 名 称：力         学 论文提交日期：2011 年 5 月 论文答辩时间：2011 年   月 学位授予日期：2011 年   月   答辩委员会主席：           评    阅    人：            厦门大学博硕士论文摘要库厦门大学硕士学位论文  厦门大学博硕士论文摘要库  Phase Field Modeling the Size Effect of Ferroelectric Thin Films by Considering the Relaxation of the Strain   A Thesis Submitted to  the Graduates School in Partial Fulfillment of the Requirements  for the Degree of Master of Engineering  By Chun-Zu ZHANG  Supervised by  Zhi-Dong ZHOU    Department of Civil Engineering School of Architecture and Civil Engineering Xiamen University  May, 2011厦门大学博硕士论文摘要库厦门大学硕士学位论文  厦门大学博硕士论文摘要库  厦门大学学位论文原创性声明  本人呈交的学位论文是本人在导师指导下,独立完成的研究成果。本人在论文写作中参考其他个人或集体已经发表的研究成果，均在文中以适当方式明确标明，并符合法律规范和《厦门大学研究生学术活动规范（试行）》。 另外，该学位论文为（                            ）课题（组）的研究成果，获得（               ）课题（组）经费或实验室的资助，在（               ）实验室完成。（请在以上括号内填写课题或课题组负责人或实验室名称，未有此项声明内容的，可以不作特别声明。）  声明人（签名）：           年   月   日  厦门大学博硕士论文摘要库厦门大学硕士学位论文  厦门大学博硕士论文摘要库  厦门大学学位论文著作权使用声明  本人同意厦门大学根据《中华人民共和国学位条例暂行实施办法》等规定保留和使用此学位论文，并向主管部门或其指定机构送交学位论文（包括纸质版和电子版），允许学位论文进入厦门大学图书馆及其数据库被查阅、借阅。本人同意厦门大学将学位论文加入全国博士、硕士学位论文共建单位数据库进行检索，将学位论文的标题和摘要汇编出版，采用影印、缩印或者其它方式合理复制学位论文。 本学位论文属于： （     ）1.经厦门大学保密委员会审查核定的保密学位论文，于   年  月  日解密，解密后适用上述授权。 （     ）2.不保密，适用上述授权。 （请在以上相应括号内打“√”或填上相应内容。保密学位论文应是已经厦门大学保密委员会审定过的学位论文，未经厦门大学保密委员会审定的学位论文均为公开学位论文。此声明栏不填写的，默认为公开学位论文，均适用上述授权。）   声明人（签名）： 年   月   日          厦门大学博硕士论文摘要库厦门大学硕士学位论文  厦门大学博硕士论文摘要库摘要  I  摘要 钙钛矿型铁电薄膜材料具有铁电性、热电性、光电性、光折变性等多种性能，被越来越多的应用于微电子领域，成为制作非易失存储器、场效应管和热电传感器等的主要材料。但铁电薄膜厚度一般在微米以下，此时薄膜的尺寸效应很强，研究铁电薄膜材料的尺寸效应具有实际的理论和应用意义。 本文基于金茨堡-朗道-德文希尔（GLD）唯象理论框架，利用等效应变模型考虑薄膜内应变松弛，同时还结合薄膜表面晶格变化引起的极化改变和表面电荷引起的退极化效应等机电耦合边界条件，应用相场法建立了金茨堡-朗道-德文希尔时间发展方程。通过线性假设分析求解了顺电相向铁电相转变初始阶段居里温度随薄膜厚度的变化，并通过有限差分法数值求解了铁电薄膜的相变温度，铁电性，相结构类型与稳定性与薄膜厚度，机电耦合边界条件等的依赖关系。结果显示，铁电薄膜在尺寸较小时，机电耦合边界条件作用明显,而尺寸较大时，薄膜性能接近于块体材料，机电耦合边界条件影响较小,即尺寸效应不明显。机电耦合边界条件是影响铁电薄膜性能尺寸效应的主要因素，而各个因素之间的相互竞争决定了薄膜的最终性能。通过分析发现，当薄膜厚度较小时，薄膜表面极化改变和电极引起的退极化效应主导薄膜铁电性的尺寸效应，而薄膜厚度较大时，薄膜内应变松弛效应是铁电薄膜铁电性趋于块体材料铁电性的主要因素。由于薄膜内存在应变松弛效应，在温度不是很高时，首次得到了较厚单畴铁电薄膜在高拉应变区会出现稳定的 c相。 对薄膜尺寸效应的分析具有实际指导意义。在实际的制备过程中，选择合适的基底可以得到性能最佳的铁电薄膜，也可通过选择生长合适的薄膜厚度，从而达到性能最佳和体积较小高集成的效果。同时，本文还提出了薄膜的铁电性，相结构和稳定性是多种边界相互竞争下的表现，进而完善了铁电薄膜相图。  关键词：铁电薄膜；尺寸效应；应变松弛；相场法 厦门大学博硕士论文摘要库厦门大学博硕士论文摘要库Abstract  IIIAbstract Ferroelectric thin films have been considerable importance in nonvolatile memory, field effect transistor, thermoelectric transducer and so on due to the ferroelectricity, thermoelectricity, photoelectricity and photorefractive properties. Generally, size effect is strong as the thickness of the films is always on nanoscale. So the investigations in this filed are significant. Basing on the Ginzburg-Landau-Devonshire (GLD) theory, the time evolution equations of GLD are obtained by considering the “effective” strain model which considers relaxation of the internal strain, together with the surface eigenstrain relaxation and depolarization field. The size effect of the transition temperature, ferroelectricity and phase stability of the ferroelectric thin films are simulated, via the analytic solutions of linear hypothesis and numerical solutions by finite difference method. The results show that the effect of the boundary conditions is obvious when the thickness of the ferroelectric thin films is small. As the thickness growing, the properties of the films are closed to the bulk and the effect of the boundary conditions is weaken, which means the size effect is weak. The boundary conditions are the principal factors of the properties of the ferroelectric thin films, and the competition between the factors decides the properties. At the small scale, the effect of the surface lattice relaxation and the electrode induced depolarization is primary. When the thickness is large enough, the effect of the relaxation of the internal strain becomes primary. It is noteworthy, at low temperature, the stability c-phase is obtained at the high tension strain because of the relaxation of the internal strain. In summary, the analysis of the size effect of ferroelectric thin films has practical significance. We can choose the appropriate thickness and the suitable substrates to design and grow the desired ferroelectric films. Here, the works also complete the phase diagrams of ferroelectric thin film.  Key words: ferroelectric thin films, size effect, relaxation of strain, phase field method 厦门大学博硕士论文摘要库厦门大学硕士学位论文   厦门大学博硕士论文摘要库目录  i目录 摘要 .................................................................................................................... I Abstract .......................................................................................................... III 第一章 绪论 ..................................................................................................................................... 1 1.1铁电材料的基本特性 .............................................................................................. 1 1.2铁电薄膜的应用 ...................................................................................................... 2 1.3研究基本理论 .......................................................................................................... 3 1.3.1金茨堡—朗道—德文希尔理论和相场法 ..................................................... 3 1.3.2软模理论和 Ising模型 ................................................................................... 4 1.3.3第一性原理 ..................................................................................................... 5 1.4铁电薄膜的发展现状 .............................................................................................. 5 1.5论文的研究内容及创新点 ...................................................................................... 8 第二章 理论分析与模型建立 ........................................................................ 9 2.1三维模型 .................................................................................................................. 9 2.2一维模型 ................................................................................................................ 12 第三章 居里温度的线性化分析 .................................................................. 14 3.1线性化假设 ............................................................................................................ 14 3.2变量分离求解 ........................................................................................................ 14 3.3数值结果与分析 .................................................................................................... 16 3.3.1薄膜厚度对相变温度的影响 ....................................................................... 17 3.3.2表面极化改变与电荷屏蔽效应对相变温度的影响（机电耦合边界条件） ........................................................................................................... 18 3.3.3内应变效应对相变温度的影响（机械边界条件） ................................... 21 3.4本章小结 ................................................................................................................ 22 第四章 铁电性能尺寸效应的非线性分析 .................................................. 24 4.1有限差分方程 ........................................................................................................ 24 4.2数值结果与分析 .................................................................................................... 26 厦门大学博硕士论文摘要库厦门大学硕士学位论文 - ii - 4.2.1温度对铁电性能的影响 ............................................................................... 26 4.2.2薄膜厚度对铁电性能的影响 ....................................................................... 28 4.2.3错配应变对铁电性能的影响 ....................................................................... 29 4.2.4表面晶格松弛和退极化效应对铁电性能的影响 ....................................... 31 4.3本章小结 ................................................................................................................ 32 第五章 单畴铁电薄膜的相结构与稳定性 .................................................. 34 5.1有限差分方程 ........................................................................................................ 34 5.2数值结果与分析 .................................................................................................... 37 5.2.1错配应变—温度相图分析 ........................................................................... 38 5.2.2错配应变—厚度相图分析 ........................................................................... 41 5.3本章小结 ................................................................................................................ 45 结论与展望 ..................................................................................................... 46 参考文献 ......................................................................................................... 48 攻读硕士期间发表的论文 ............................................................................ 53 致谢 ................................................................................................................. 54  厦门大学博硕士论文摘要库Table of Contents  iiiTable of Contents Abstract in Chinese .......................................................................................... I Abstract .......................................................................................................... III Chapter 1  Instroduction .............................................................................. 1 1.1  Fundamental Characteristics of Ferroelectric Material .................................. 1 1.2  Application of Ferroelectric Thin Films ............................................................ 2 1.3  Basic Theories of Research .................................................................................. 3 1.3.1  Theory of Ginzburg-Landau-Devonshire and Phase Field Method ............. 3 1.3.2  Theory of Soft Mode and Ising Model ......................................................... 4 1.3.3  First Principle ............................................................................................... 5 1.4  Status of Ferroelectric Thin Films ...................................................................... 5 1.5  Content and Innovation of the Research ........................................................... 8 Chapter 2  Theories Discussing and Modeles Building ............................. 9 2.1  3 Dimensional Model ........................................................................................... 9 2.2  1 Dimensional Model ......................................................................................... 12 Chapter 3  Linear analysis of Curie Temperature ................................... 14 3.1  Linear Hypothesis .............................................................................................. 14 3.2  Solution of Separarion of Variables .................................................................. 14 3.3  Numerical Results and Discussion .................................................................... 16 3.3.1  Effect of Film Thickness on Phase Transiton Temperature ....................... 17 3.3.2  Effect of Surface Eigenstrain Relaxation and Depolarization Field on Phase Transiton Temperature .................................................................... 18 3.3.3  Effect of Internal Strain on Phase Transiton Temperature ......................... 21 3.4  Brief Summary ................................................................................................... 22 Chapter 4  Nonlinear Analysis of Size Effect of Ferroelectricities ......... 24 4.1  Equations of Finite Difference .......................................................................... 24 4.2  Numerical Results and Discussion .................................................................... 26 厦门大学博硕士论文摘要库厦门大学硕士学位论文 - iv - 4.2.1  Effect of Temperature on the Ferroelectricities .......................................... 26 4.2.2  Effect of Film Thickness on the Ferroelectricities ..................................... 28 4.2.3  Effect of Misfit Strain on the Ferroelectricities ......................................... 29 4.2.4  Effect of Surface Eigenstrain Relaxation and Depolarization Field on the Ferroelectricities .................................................................................. 31 4.3  Brief Summary ................................................................................................... 33 Chapter 5  Phase Stability of Single Domain Epitaxial Ferroelectric films ......................................................................................... 34 5.1  Equations of Finite Difference .......................................................................... 34 5.2  Numerical Results and Discussion .................................................................... 37 5.2.1  Discussion of the Phase Diagrams of Misfit Strain-Temperature .............. 38 5.2.2  Discussion of the Phase Diagrams of Misfit Strain-Thickness .................. 41 5.3  Brief Summary ................................................................................................... 45 Conclutions and Prospect ............................................................................. 46 References ...................................................................................................... 48 Publications during the Course of the Work .............................................. 53 Acknowledgements ........................................................................................ 54   厦门大学博硕士论文摘要库Degree papers are in the “Xiamen University Electronic Theses and Dissertations Database”. Fulltexts are available in the following ways: 1. If your library is a CALIS member libraries, please log on http://etd.calis.edu.cn/ and submitrequests online, or consult the interlibrary loan department in your library. 2. For users of non-CALIS member libraries, please mail to etd@xmu.edu.cn for delivery details.厦门大学博硕士论文摘要库

Phase Field Modeling the Size Effect of Ferroelectric Thin Films by Considering the Relaxation of the Strain

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Phase Field Modeling the Size Effect of Ferroelectric Thin Films by Considering the Relaxation of the Strain

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