Computational Study of O Vacancy and La Dopant in HfO2 and their Effect on the Adsorbed Graphene Layer

本研究運用第一原理計算結合古典力場方法與分子動態模擬來探討二氧化鉿中氧空缺與鑭摻雜的基本性質以及其對石墨烯電子性質之影響。 在第一部分的研究中，我們利用第一原理計算產生包含二氧化鉿結構、機械與介電性質等的資料庫，並依此建構同時適用立方晶相及正方晶相二氧化鉿的原子力場模型。接著我們透過相位穩定度、相轉變溫度以及氧空缺在二氧化鉿中遷移能等計算來驗證此力場模型的可靠性與移轉性，而計算結果顯示利用力場模型預測的性質與第一原理計算所得性質相當接近。 在第二部分的研究中，我們利用第一原理計算探討鑭摻雜對結晶相二氧化鉿結構、電子與介電性質的影響。計算結果顯示，鑭摻雜可減小正方晶相與單斜晶相二氧化鉿之間的能量差，因而增加了正方晶相二氧化鉿的穩定度與出現機率。同時我們也發現由於鑭摻雜會導致氧空缺的形成與二氧化鉿對稱性的下降，此材料系統的彈性模數會因而下降，增加了正方晶相二氧化鉿被應力誘發而穩定的現象之發生機率，為正方晶相二氧化鉿在文獻上實驗高溫退火過程中的出現提供了合理的物理解釋。另外，研究結果顯示鑭摻雜可以在維持足夠能隙值的情況下，提高二氧化鉿材料的介電常數，而這主要是由於鑭摻雜會使系統的特性力常數下降的緣故。 文獻實驗結果顯示，以二氧化鉿做為基材會大幅降低吸附於其上之石墨烯的傳導性質，因此在第三部分的研究中我們嘗試運用第一原理計算研究二氧化鉿基材對石墨烯電子性質的影響。結果顯示石墨烯會以凡得瓦作用力吸附於二氧化鉿基材上，且其吸附能量約較在二氧化矽基材上大25~40%，而石墨烯在狄拉克點產生的能隙值與吸附在含有silanol group二氧化矽基材表面接近，但其與基材間產生的電荷重新分布量則比二氧化矽基材大了一個數量級。此外，當石墨烯吸附在含有氧空缺的二氧化鉿基材時，電子會由基材中氧空缺位置轉移到石墨烯上使得石墨烯產生n型摻雜效果，且氧空缺與石墨烯之間強烈的交互作用不僅會在狄拉克點附近造成較大的能隙值，亦會破壞石墨烯能帶結構的線性分布。然而我們也發現當有水吸附於二氧化鉿基材表面時，氧空缺所導致的石墨烯n型摻雜效果可能會被減弱，甚至轉變為p型摻雜效果。最後，我們的計算結果顯示，鑭摻雜在二氧化鉿基材中或許能成為一種有效改善其上吸附之石墨烯傳導性質的方法。In this study, we performed first principles calculations in conjunction with classical force field method and molecular dynamics simulations to investigate the fundamental properties of oxygen vacancy and La dopants in HfO2 as well as their effect on the electronic properties of the adsorbed graphene layer. In the first part of the thesis, we present our newly-developed atomistic potential model for the cubic and tetragonal phases of HfO2. This new potential model was developed based on the ab initio calculated database, including the structural, mechanical, and dielectric properties of the cubic and tetragonal phases of HfO2, respectively. The reliability and transferability of this newly-developed model for HfO2 has been examined through a series of validations, such as the relative phase stability between c- and t-HfO2, the phase transition temperature, and the migration energy barrier of O vacancy in HfO2. Our calculated results show that all the predictions are in satisfactory agreement with the first-principles predicted properties of the cubic and tetragonal phases of HfO2. In the second part of the thesis, we performed first principles calculations to investigate the effect of La doping on the structural, electronic and dielectric properties of crystalline HfO2. Our calculated results show that the thermodynamic stability of tetragonal HfO2 relative to its monoclinic phase can be enhanced via doping with the substitutional La atoms. Our calculations also show that the elastic moduli of HfO2 can be lowered by La doping, which could be ascribed to the lowering of the symmetry and the associated formation of O vacancy in the HfO2 matrix. Moreover, this softening of material matrix also indicates that the possibility of the stress-induced stabilization of the tetragonal phase of HfO2 can be enhanced via La doping, providing a physical origin for the appearance of t-HfO2 during high temperature annealing in the experiments. On the other hand, our calculated results also show that the substitutional La doping can increase the dielectric constant of HfO2 while still maintaining sufficient electronic band gap, which was found to be mainly attributed to the reduction of the characteristic force constant of the dielectric material system. In the third part of the thesis, we performed first principles study on the electronic properties of graphene monolayer on the HfO2 substrate. Our main research interest here is to understand why the HfO2 substrate can significantly degrade the transport properties of the adsorbed graphene layer as revealed in the experiments. Our calculated results show that graphene monolayer is bounded to a perfect HfO2 surface via the van der Waals interaction with a binding energy of around 25~40% larger than that on the SiO2 substrate. The band gap opening at the Dirac point was found to be comparable to that on a silanol SiO2 surface, but the induced charge accumulation at the graphene/HfO2 interface is at least one order of magnitude larger than that between graphene and the silanol surface. Moreover, when graphene monolayer was placed on top of the substrate containing an O vacancy, the adsorbed graphene layer becomes n-type doped primarily due to the charge transfer from the O vacancy site in the HfO2 substrate. Our results further show that the strong interaction between O vacancy and the graphene layer not only can result in a relatively larger band gap opening at the Dirac point but also can degrade the linear band dispersion in the band structure of monolayer graphene. More interestingly, our calculations show that the O vacancy induced n-type doping on graphene can be reduced or eventually turn into p-type doping when there are water molecules adsorbed on the HfO2 surface. In addition, our calculations also suggest that La doping in HfO2 can be an effective approach towards improving the transport properties of the adsorbed graphene layer on the HfO2 substrate.摘要 i Abstract iii Contents v List of Figures vii List of Tables xiii Chapter 1. Introduction 1 Chapter 2. Theoretical Background 5 2.1 First principles calculation 5 2.2 Density functional theory (DFT) 5 2.2.1 Thomas-Fermi model 6 2.2.2 Hohenberg-Kohn theorem 6 2.2.3 Kohn-Sham equation 7 2.2.4 Exchange-correlation functional 9 2.2.5 Hybrid density functional 9 2.2.6 Van der Waals density functional 10 2.2.7 Pseudopotential 11 2.3 Classical force field 12 2.3.1 Buckingham potential 13 2.3.2 Core-shell model 13 2.3.3 Potential parameters optimization 14 2.4 Molecular dynamics 14 2.4.1 Verlet algorithm 15 2.4.2 Nose-Hoover thermostat 15 Chapter 3. Development of Atomistic Potential Model for HfO2 in Cubic and Tetragonal Phases 17 3.1 Introduction 17 3.2 Potential model 21 3.3 Bulk properties 24 3.4 Validation properties 28 3.4.1 Phase stability 28 3.4.2 Phase transition temperature 29 3.4.3 Oxygen vacancy migration energy 31 3.5 Summary 37 Chapter 4. The Structural, Electronic and Dielectric Properties of La-doped HfO2 39 4.1 Introduction 39 4.2 Effect of La doping on the structure of HfO2 43 4.3 Effect of La doping on phase stability of HfO2 50 4.4 Electronic and dielectric properties of La-doped HfO2 55 4.5 Summary 66 Chapter 5. The Electronic Properties of Graphene Adsorbed on HfO2 Surface 67 5.1 Introduction 67 5.2 Electronic properties of graphene 69 5.3 Graphene on pure HfO2 substrate 72 5.3.1 Perfect HfO2 substrate 74 5.3.2 HfO2 substrate with oxygen vacancy 80 5.4 The presence of H2O in the interface between graphene and HfO2 87 5.4.1 H2O physical adsorption on HfO2 surface 89 5.4.2 H2O dissociation on HfO2 surface 95 5.5 Graphene on La-doped HfO2 substrate 104 5.6 Graphene on amorphous substrate 112 5.7 Summary 117 Chapter 6. Conclusion 119 Reference 12