【作者】 张超；

【导师】 王春雷；

【作者基本信息】 山东大学 ， 凝聚态物理， 2007， 硕士

【摘要】 目前，铁电材料同时具有压电，热释电，电光，声光，光折变和非线性光学效应，因此它们在微电子和光电子领域获得了大量的应用。现在，由铁电材料制成的器件在人们日常生活中发挥着不可替代的作用。基于铁电材料的重要性，因此了解这类材料不同形态的物理性质具有重要的学术价值。近年来，很多理论方法，包括朗道唯象理论和原子层次上的第一性原理计算，被广泛地用来研究铁电材料的性质。随着密度泛函理论和计算机硬件的不断发展，利用第一性原理方法计算电子结构和结构动力学已成为研究铁电体的一个常规方法。与实验中材料合成的进展相平行，在过去几十年中，有关铁电体原子层次的理论计算也有了长足的发展，尤其是关于钙钛矿氧化物的第一性原理研究。起初，人们的研究重点在块状铁电材料。第一性原理计算极大地帮助人们了解铁电结构的起源以及铁电不稳定性的内部机制。有关这一方面的主要成果是，利用密度泛函理论在Born-Oppenheimer近似的框架下计算基态能量，并由此得出基态晶格结构，声子色散关系，以及弹性常数。近几年来，第一性原理计算被逐渐扩展到复杂体系（例如掺杂体系，超晶格和固溶体等）和低维体系（例如固体表面，纳米管，量子阱以及量子点等）。在第一性原理的框架下模拟，可以清楚地确定问题，并针对问题进行研究分析。所以，理论分析不仅解释了复杂铁电体系的实验现象，而且为实验提供了一定的指导。本论文把这种方法应用到了钙钛矿型铁电材料的表面结构和掺杂体系。在计算中，主要采用了ESPRESSO软件包和Castep程序。ESPRESSO软件包是基于密度泛函理论，利用平面波赝势法（PWP）计算电子结构的程序。Castep程序是Material Studio的一个模块，它也是利用了平面波赝势法。下面列出了本论文展开的主要内容：（1）对立方相BaZrO₃（001）表面的研究，包括以BaO和以ZrO₂为终结面的两种表面结构。通过计算得到了表面结构，态密度，能带结构以及表面能。发现最大的表面弛豫发生在第一层原子，以BaO为终结面的表面弛豫要比以ZrO₂为终结面的表面弛豫大。以BaO为终结面的表面褶皱也比以ZrO₂为终结面的表面褶皱大。相对于块状材料，两种表面类型的带隙都减小了，带隙的减小主要来在表面层的O 2P和Zr 4d电子。表面能的结果显示BaZrO₃的表面比PbZrO₃的表面更稳定。（2）对铁电体掺杂体系的研究。利用第一性原理研究了Fe掺杂BaTiO₃和SrTiO₃。计算得到了杂质形成能，晶格畸变，能带结构和态密度。发现Fe掺杂BaTiO₃和SrTiO₃的杂质形成能分别是6.8eV和6.5eV。Fe杂质和它最近邻的O原子之间的距离以及Fe杂质和Ba或Sr原子之间的距离都比块状材料的相应距离变小了。对于两种材料而言，在导带和价带之间都出现了Fe掺杂能级，Fe掺杂能级主要源于Fe 3d电子。对Nb掺杂SrTiO₃电子结构的研究。得到了杂质形成能，结构畸变，能带结构和态密度。杂质形成能的结果显示Nb更倾向于替位SrTiO₃中Ti的位置，这与实验上符合得很好。经过Nb掺杂后，SrTiO₃体系的费密能级移动到导带的底部，SrTiO₃体系经过了绝缘体到金属的转变。由于来自Nb杂质的载流子使得价带顶部发生了明显的畸变。对于Fe掺杂CaTiO₃电子性质和结构性质的研究。采用了平面波赝势法（PWP），计算得到了杂质的形成能，结构优化参数，能带结构和态密度。杂质的形成能显示Fe更倾向于替换CaTiO₃中Ti的位置，这与实验上的结果是相符合的。此外，还发现Fe杂质的引入对晶格结构影响较小，只是引起了局域结构畸变。在导带和价带之间出现了Fe掺杂能级，但更接近于价带。Fe掺杂能级主要源于Fe 3d电子。杂质能级在整个布里渊区中的色散是微弱的，最明显的色散在X点。更多还原

【Abstract】 Ferroelectrics have been widely used in the field of microelectronics and optoelectronics since they exhibit many excellent properties such as piezoelectricity, thermoelectricity, electro-optic, photorefractive and nonlinear optical effect. Nowadays, the presence of ferroelectric devices is practically indispensable in everyday’s life. Therefore, understanding the physical properties of ferroelectrics is academically significant and practically important.In recent years, different theoretical approaches, including phenomenological Landau theories and atomic-level first-principles calculations, have been used to study the physical properties of ferroelectrics. With continuing advances in density functional theory （DFT） and computer hardware, first-principles studies of electronic structure and structural energetics have become a routine method for ferroelectrics. In parallel with advances in materials synthesis, it has seen a revolution in the atomic-scale theoretical understanding of ferroelectricity in the past decade, especially in perovskite oxides, through first-principles density functional theory investigations. At early stage, people mainly focused on properties in bulk ferroelectrics. First-principles calculations have greatly contributed to the understating of the origin of ferroelectric structures and properties and to mechanisms of ferroelectric instabilities. The central result of a density functional theory calculation is the ground-state energy computed within the Born-Oppenheimer approximation; from this the predicted ground-state crystal structure, phonon dispersion relations, and elastic constants are directly accessible. Recently, first-principles calculations are gradually extended to complex systems, such as doped systems, superlattices and solid solutions, and low demission systems, such as solid surface, nanotube, quantum well and quantum dots. Within this first-principles modeling framework, it can be more clearly identify specific issues and results for investigation and analysis. So, theoretical analysis not only explains observed properties of complex systems of ferroelectrics, but also provides instructions for experiment. In this dissertation, this method has been applied to study the surface structure and doped systems of perovskite-type ferroelectrics. Calculations are mainly carried out using ESPRESSO package and Castep program which is a module of Material Studio. ESPRESSO package is a set of programs for electronic structure calculations within DFT, using a plane-wave basis set and pseudopotentails. Also, Castep program is using a plane-wave basis set and ultra-pseudopotentials.In this following, I summarize the main contents of my dissertation. Investigation of the （001） surface of cubic BaZrO₃ with BaO and ZrO₂ terminations. Surface structure, partial density of states, band structure and surface energy have been obtained. It is found that the largest relaxation appears on the first layer of atoms, and the relaxation of the BaO-terminated surface is larger than that of the ZrO₂-terminated surface. The surface rumpling of the BaO-terminated surface is also larger than that of the ZrO₂-terminated surface. A reduction of the band gap has been found for both kinds of surface terminations, and the reduction is mainly due to the O 2p and Zr 4d electrons at the surface layers. Results of surface energy calculations reveal that the BaZrO₃ surface is likely to be more stable than the PbZrO₃ surface.Study of doped systems of ferroelectrics. First principles calculations have been performed on Fe-doped BaTiO₃ and SrTiO₃. Dopant formation energy, structure distortion, band structure and density of states have been computed. The dopant formation energy is found to be 6.8 eV and 6.5 eV for Fe-doped BaTiO₃ and SrTiO₃ respectively. The distances between Fe impurity and its nearest O atoms and between Fe atom and Ba or Sr atoms become smaller than those of the corresponding undoped bulk systems. The Fe defect energy band is obtained, which mainly originates from Fe 3d electrons.Electronic and structural properties of Nb-doped SrTiO₃ are studied using the first principles density functional theory （DFT） calculations based on a plane-wave basis and pseudopotentials. Dopant formation energy, structure distortion, band structure as well as density of states have been obtained. Dopant formation energy results show that Nb preferentially enters the Ti site in SrTiO₃, which is good agreement with experimental observations. The Fermi level of the Nb-doped SrTiO₃ move into the bottom of conduction band, and the system undergoes an insulator-to-metal transition. Due to the appearance of the carrier impurity from Nb doping, there is a significant distortion on the top valence band.An investigation of electronic and atomic structural properties of Fe-doped CaTiO₃ has been performed using first-principles density functional theory （DFT） calculations based on a plane-wave basis and pseudopotentials. Dopant formation energy, structure distortion, band structure and density of states have been obtained. It is shown from the dopant formation energy that Fe preferentially enters the Ti-site in CaTiO₃ , which is good agreement with experimental data. Also Fe doping leads to a small local structural distortion. The Fe defect energy band appears between conduct band and valence band, but closer to the valence band. This Fe defect energy mainly originates from Fe 3d electrons. The defect band dispersion is weak throughout the Brillouin zone, and the most distinct dispersion lies at the X point.更多还原