【作者】 何建平；

【导师】 吕文中；

【作者基本信息】 华中科技大学 ， 微电子学与固体电子学， 2012， 博士

【摘要】 钛酸锶钡(Ba_xSr_1-xTiO₃, BST)具有介电常数调节方便、较低的介电损耗以及电场作用下高介电常数非线性等良好的介电性能，在可调介质滤波器和移相器等微波调谐器件方面有着广泛的应用。本文以钛酸锶钡为研究对象，采用基于密度泛函理论的第一性原理方法对其结构以及极化特性进行理论计算研究，同时结合实验观察钛酸锶钡的极化和电畴变化。首先以五种有序结构模型为代表，使用第一性原理方法对立方相结构的Ba_xSr_1-xTiO₃（x=0.125,0.25,0.5,0.75,0.875）进行了详细的计算研究。结果表明平衡晶格常数和组分含量x之间呈现线性变化规律，符合Wegard定律。在立方相有序结构Ba_xSr_1-xTiO₃（x=0.125,0.875）中，出现Ti原子和O原子的偏心位移，导致Ti-O八面体产生畸变。这将导致4对反平行且互相成109°夹角的自发极化的产生，但由于这4对极化的大小相同、方向相反，所以不会引起宏观的极化，而且晶格结构仍保持为立方相。对态密度和差分电荷密度的分析表明，BST中Ti3d和O2p电子之间的轨道杂化作用强于Ba和O以及Sr和O轨道电子之间的杂化作用，特别是在价带顶和导带底的高能量区间。在BST中，Ba-O和Sr-O之间是离子相互作用，而Ti-O间则是强烈的共价相互作用。Ti和O原子之间的共价相互作用，特别是Ti3d和O2p电子之间的轨道杂化作用，是BST自发极化以及铁电性产生的主要因素。然后对Ba_0.25Sr_0.75TiO₃、Ba_0.5Sr_0.5TiO₃以及Ba_0.75Sr_0.25TiO₃这三种组分均分别建立了三种有序结构模型，根据这些A位的Ba和Sr原子有序分布的模型，主要对它们进行结构上的第一性原理计算分析研究。其中的BST0.25<010>、BST0.25<011>、BST0.5{100}、BST0.75<010>以及BST0.75<011>这些有序结构晶胞都处于四方相反铁电态，而BST0.5{110}这个有序构型处于四方顺电相，BST0.25<111>、BST0.5{111}和BST0.75<111>这三个有序构型为立方顺电相。可见在BST中，A位的局部有序性对无序结构BST固溶体的结构相变是一个重要的影响因素，可以导致从四方相反铁电态到四方相顺电态以及立方相顺电态的变化。接着以Ba_0.5Sr_0.5TiO₃的三种有序构型——BST{100}、BST{110}和BST{111}为研究对象，采用第一性原理方法，计算分析Ti-O八面体中Ti原子的偏心位移对BST的原子构型和极化特性的作用和影响。进而了解在BST铁电体中，外加电场作用下所引起的Ti和O原子的偏心位移，对BST的原子构型和自发极化的影响以及作用的机理。在BST{100}、BST{110}和BST{111}有序构型中，当Ti原子分别在x方向、z方向和z方向上，即BST晶格的二重轴或者更高重轴所在方向偏心位移时，计算得到的稳定晶格结构均为四方相，同时都出现自发极化，结构处于四方相铁电态。而当BST{100}和BST{110}有序构型中的Ti原子分别在z方向和x方向上（不是BST晶格的二重轴或者更高重轴所在方向）偏心位移时，得到的稳定晶格结构均为正交相，同时也都出现自发极化，结构处于正交相铁电态。可见外加电场作用下所引起的Ti原子的偏心位移，可以引起晶格的畸变和Ti-O八面体的畸变，产生自发极化，从而使得BST发生结构相变，而且所加外电场方向决定了相变后的铁电相的结构。最后使用压电响应力显微技术（PFM），同时结合透射电子显微镜（TEM），对外加直流电场作用下Ba_xSr_1-xTiO₃（x=0.3,0.6,0.9）铁电体中的电畴诱导演变以及极化反转进行了实验观察研究。结果发现，在无外加直流偏压的情况下，BST铁电材料顺电相结构中不存在铁电畴，也不存在由于相变扩张所导致的铁电微区。而当对顺电体外加直流偏压时，BST铁电材料(Ba_0.6Sr_0.4TiO₃)中可以诱导出铁电畴，并对顺电相BST铁电体中非线性介电特性产生贡献。第四章中得出的第一性原理的理论计算结果，即由电场作用引起的Ti离子位移会导致极化的产生并引起结构相变，在此处得到了一定的实验验证。同时，对处于顺电相的BST铁电材料而言，外加电场诱导出铁电畴的难易程度与其居里温度有关，居里温度越高，外电场作用下越容易诱导出铁电畴。在方向相反的直流偏压下，可以观察到BST铁电体(Ba_0.9Sr_0.1TiO₃)中的电畴会发生极化反转。而且在不同大小的直流偏场下诱导出的铁电畴呈现渐进的变化，这说明BST铁电体中的电畴是一个会随外场而变化的动态过程，这一动态过程导致了BST铁电体中非线性介电特性的产生。更多还原

【Abstract】 Due to the highly nonlinear dielectric response to an applied electric field, moderatedielectric constant and low dielectric loss in microwave domain, barium strontium titanate(Ba_xSr_1-xTiO₃, BST) is a promising material for electric tunable devices for microwaveapplications, such as tunable dielectric filters and phase shifters. BST is chosen as researchobject in this dissertation. The structure and polarization of BST were investigated byfirst-principles calculations based on density-functional theory. Furthermore, thepolarization and domain structure of BST were studied by piezoresponse force microscopy（PFM） and transmission electron microscop （TEM）.Firstly, the first-principles calculations of the five different BST ordered structureswere performed. It is found that the lattice constants show a linearly increase with x, whichis consistent with Vegard’s law. The off-center displacement of Ti atoms and O atomsresults in the distortion of Ti-O octahedron, and four pairs antiparallel spontaneouspolarization induced in Ba_xSr_1-xTiO₃（x=0.125,0.875）. Therefore this two equilibriumordered structures are both in cubic antiferroelectric phase.The analyses of the density of states and electron density difference shows that thehybridization between Ti3d and O2p is stronger than that between Ba （or Sr） and O.Especially in the high energy region near valence band maximum and conduction bandminimum. The interactions of Ba-O and Sr-O are ionic, while the Ti-O bond is covalent inBST. Based on above analysis, it concludes that the hybridization between Ti3d and O2pplays primary role in the generation of spontaneous polarization and ferroelectricity.Secondly, every three different ordered structures of Ba_0.25Sr_0.75TiO₃, Ba0.5Sr0.5TiO₃and Ba_0.75Sr_0.25TiO₃were constructed, and nine in total. The results of the first-principlescalculations of the nine different BST ordered structures indicate that all of the equilibriumordered structures of BST0.25<010>, BST0.25<011>, BST0.5{100}, BST0.75<010> andBST0.75<011> are in tetragonal antiferroelectric phase. And the BST0.5{110} orderedstructure is in tetragonal paraelectric phase, all of the ordered structures of BST0.25<111>,BST0.5{111} and BST0.75<111> are in cubic paraelectric phase. The results of the presentwork implied that the local order of A site cations significantly influence the structuralphase transition of disordered BST solid solution.Thirdly, based on the three different ordered structures of Ba_0.5Sr_0.5TiO₃, namely BST{100}, BST{110} and BST{111}. An off-center displacement of Ti atoms along thefour fold axis of Ti-O octahedron introduce into BST by0.05in fractional coordinate. Andthen the first-principles calculations of the five different structures with the off-centerdisplacement of Ti atoms were run. All the three structures BST{100}, BST{110} andBST{111} with Ti atoms respectively moving along the x, z and z are in tetragonalantiferroelectric phase. And the other two structures BST{100} and BST{110} with Tiatoms respectively moving along the z and x are in orthorhombic antiferroelectric phase. Inconclusion, the off-center displacement of Ti atoms could cause the distortion of BST latticsand Ti-O octahedron, and the structure phase transition of BST occurs.Lastly, The character of the domain structures in Ba_xSr_1-xTiO₃（x=0.3,0.6,0.9）ceramics prepared by the solid-state reaction was investigated by piezoresponse forcemicroscopy （PFM） and transmission electron microscopy （TEM）. The PFM results indicatethat the domains could be induced in paraelectric phase Ba0.6Sr0.4TiO₃under dc voltageapplied between the tip and the bottom electrode. And when the Curie temperature of BSTis higher the induction of the domains is easier. The polarization reversal occurs inBa0.9Sr0.1TiO₃after the application of reverse dc bias voltage. Furthermore, the patterns ofdomains in BST could change with the value of the dc bias voltage. And the dynamicdevelopment of domains in BST would cause the nonlinear dielectric properties ofparaelectric phase BST ceramic.更多还原