针对PFM技术的铁电材料纳米尺度力电耦合分析

发布时间：2018-03-04 12:37

本文选题：压电响应力显微技术(PFM)　切入点：压电材料　出处：《湘潭大学》2014年博士论文　论文类型：学位论文

【摘要】：压电、铁电材料因具有优异的力电耦合性能，而广泛的应用于各类微电子器件。近年来，压电响应力显微技术(PFM)已经发展成为在纳米尺度无损表征压电、铁电等极性材料的重要工具。但是，基于PFM的定量分析存在很大的困难，而且相应的研究极富挑战性。本论文主要针对PFM技术定量分析的相关问题展开研究，包括导电探针与压电材料间的电弹性场分析，压电系数定量分析，静态铁电畴成像，以及PFM对纳米尺度铁电畴结构分辨率分析。基于发展的数值解耦方法和全耦合方法，定量分析PFM中的力电耦合效应。研究内容包括以下几个方面：第一，发展了数值解耦方法并提出了新的全耦合方法，用于分析导电SPM探针与样品间的电弹性场。首先，基于解耦格林函数理论，提出了数值积分方法，发展了现有的解耦格林函数方法。另外，通过空气和压电材料间的耦合作用，发展了一套新的力电全耦合方法。其次，，基于这两种方法我们分析了压电材料内的电弹性场分布。最后，针对不同几何形状的针尖，提出了全耦合方法的针尖模型。结果表明，电场和位移场都具有高度的局域性和非均匀性，而且全耦合方法对应的电势在压电材料半空间衰减更快，从而针尖附近电场较大，但是位移则相应较小。不同针尖模型电场集中度不同，但是位移响应与针尖模型无关，而是取决于计算采用的是解耦方法，还是耦合方法。第二，考虑PFM的接触模式和非接触模式，分析了压电系数定量分析困难的原因，并提出了准确定量分析压电系数的两种新方法。首先，考虑PFM测试为接触模式，基于解耦方法和全耦合方法，分析了有效压电系数与材料本征参数的关系。其次，我们提出了PFM测试的非接触模式，分析了有效压电系数与测试条件的关系。最后，我们提出了两种定量分析纳米尺度压电系数的新方法，即双针头测试方法和反演优化材料参数方法。结果表明，有效压电系数与材料本征电弹性常数和测试条件密切相关，甚至具有非线性关系，使得定量分析压电系数非常困难。然而，我们提出的双探针方法和反演优化方法都能实现对分析压电系数的准确定量分析。第三，基于解耦格林函数方法，发展分区数值积分方法，分析了PFM技术对非均匀静态铁电畴结构的成像。以180度畴、90度畴和复杂铁电畴为例，分析了极化非均匀性对PFM振幅和相位响应的影响。结果表明，PFM位移响应取决于材料内部三维的极化分布，因而重构三维铁电畴结构，则必需已知VPFM和LPFM的振幅和相位响应。第四，基于相位响应，分析了PFM对纳米尺度铁电畴结构的分辨率。我们分别以180度面外畴和90度畴，以及180度面内畴为例，分析了畴界响应半宽与针尖半径关系，进而分析VPFM和LPFM对纳米铁电畴的分辨能力。同时，还探讨了PFM对内部铁电畴的分辨能力。结果表明，PFM分辨率取决于畴界响应半宽，VPFM比LPFM的分辨率更高。而且PFM还能分辨内部铁电畴结构，但是对深度非常敏感。本论文发展了数值解耦方法和全耦合方法，实现了对PFM中力电耦合问题的纳米尺度定量分析。这为未来分析异质铁电材料以及动态畴翻转等问题打下了坚实的基础。
[Abstract]:Piezoelectric and ferroelectric materials because of the excellent performance of electromechanical coupling, and widely used in all kinds of microelectronic devices. In recent years, piezoresponse force microscopy (PFM) has become the nondestructive characterization of piezoelectric in nanometer scale, an important tool for ferroelectric polar materials. However, the quantitative analysis is based on the PFM great difficulties and challenging research accordingly. This thesis focuses on the issues related to quantitative analysis of PFM technology is studied, including the conductive probe and the piezoelectric material of the electric elastic piezoelectric coefficient field analysis, quantitative analysis, static ferroelectric domain imaging, and PFM on the nanoscale resolution analysis. Numerical decoupling the development and the full coupling method based on quantitative analysis of electromechanical coupling effect in PFM. The study includes the following aspects:
First, the development of numerical decoupling method and put forward the whole new coupling method, for the analysis of conductive SPM probe and the sample of the electric elastic field. Firstly, decoupling theory of Green function based on the proposed numerical integration method, the development of the existing methods of decoupling Green function. In addition, through the interaction of air and piezoelectric materials the development of a new set of mechanical and electrical coupling method. Secondly, based on these two methods, we analyzed the electro elastic piezoelectric materials in the field. Finally, according to the different geometry of the tip, put forward the model of tip coupling method. The results show that the electric field and displacement field are highly localized and non uniformity, and potential corresponding to full coupling method in piezoelectric half space attenuation faster, so the electric field near the tip is larger, but the displacement is smaller. The different tip model of electric field concentration is different, but the displacement The response is independent of the pinpoint model, but depends on whether the calculation is used as a decoupling method or a coupling method.
Second, consider the PFM contact mode and non contact mode, analyzes the piezoelectric coefficient of quantitative analysis of the reasons for the difficulties, and puts forward two new methods for piezoelectric coefficient quantitative analysis. Firstly, considering the PFM test for contact mode, decoupling method and coupling method based on the analysis of the relationship between the intrinsic parameters of piezoelectric coefficient and materials. Secondly, we put forward the non contact mode PFM test, analysis of the relationship between effective piezoelectric coefficient and the testing conditions. Finally, we put forward a new method of piezoelectric coefficient of nano scale two quantitative analysis, namely double needle test method and material parameter inversion optimization method. The results show that the effective the piezoelectric coefficient and intrinsic electric elastic constants and test conditions are closely related, and even has a nonlinear relationship, makes quantitative analysis of the piezoelectric coefficient is very difficult. However, the double probe of our proposed method and inverse optimization method The accurate quantitative analysis of the analytical piezoelectric coefficient can be achieved.
Third, decoupling based on Green function method, development division numerical integral method, analysis of PFM imaging technology on non uniform static ferroelectric domain structure. Based on the 180 degree domain, 90 degree domain and complex domain as an example, analyzes the polarization effects of nonuniformity on PFM amplitude and phase response. The results show that the displacement of PFM the response depends on the polarization distribution in the material internal three-dimensional, three-dimensional reconstruction and ferroelectric domain structure, it is necessary to amplitude and phase of the known VPFM and LPFM response.
Fourth, based on the phase response analysis of PFM resolution on the nanoscale structure. We were at 180 degrees and 90 degrees out of plane domain domain, and 180 degree plane domain as an example, analyzes the relationship between the half width and tip radius response boundary, and analysis of resolution of VPFM and LPFM on nano ferroelectrics at the same time, also discussed the resolution of internal PFM ferroelectric domain. The results show that the PFM resolution depends on the boundary of the half width of the VPFM response, a higher resolution than the LPFM. But PFM can distinguish internal ferroelectric domain structure, but very sensitive to depth.
The numerical decoupling method and the fully coupled method have been developed in this paper to achieve the nanoscale quantitative analysis of the electromechanical coupling in PFM. This will lay a solid foundation for future analysis of heterogeneous ferroelectric materials and dynamic domain upset.

【学位授予单位】：湘潭大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM221;TB383.1

【参考文献】