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論文名稱 Title |
運用第一原理研究超薄鉍薄膜在鍺(111)和矽(111)的原子結構和電子結構 First-principles studies of atomic structures and electronic properties of Bi ultrathin films on Si(111) and Ge(111) |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
83 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2013-06-07 |
繳交日期 Date of Submission |
2013-07-23 |
關鍵字 Keywords |
鍺(111)、矽(111)、第一原理、拓樸絕緣體、鉍薄膜、沈呂九、陳省身 Kohn-Sham, Ge(111), Si(111), topological insulator, first-principles, ultrathin bismuth films, Chern number |
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統計 Statistics |
本論文已被瀏覽 5730 次,被下載 568 次 The thesis/dissertation has been browsed 5730 times, has been downloaded 568 times. |
中文摘要 |
我們利用第一原理的方法研究1/3 單層(ML)到5 單層(ML)的鉍原子吸附在半導體基板矽(111)和鍺(111)的原子結構。鉍原子結構為皺摺蜂窩狀的自由獨立雙層時,可以知道為二維拓樸絕緣體。另一方面,1ML 的鉍原子在矽(111)和鍺(111)的穩定結構之前已經有詳細的研究了,表面都有很強的Rashba 效應。因此,超薄鉍薄膜生長在基本上是一個有趣且重要的課題。我門的計算結果發現在鍺(111)基板上,3ML 和5ML 的鉍有機會長出拓樸絕緣體結構。但是鉍雙層結構的電子會轉移到基板上,對鉍雙層結構造成p 型電子參雜,這種p 型參雜的作用會平移費米面也破壞了拓樸性質。相較於矽(111)的表面,在3ML 和5ML 時最上層就沒有形成拓樸絕緣體的結構,主要原因為矽對鉍的壓縮比鍺還要大。 |
Abstract |
The atomic and electronic structures of ultrathin bismuth films on Si(111) and Ge(111) surface were investigated using first-principles calculations at Bi coverages ranging from 1/3 ML to 5 MLs. The free standing bismuth bilayer is in buckled honeycomb structure and has been previously identified as is a two dimensional topological insulator. On the other hand, at 1 ML, the reconstructed Si(111) and Ge(111) have been previously studied and exhibits strong Rashba splitting at the M point. Thus, it is very interesting and important to study the Bi ultrathin films on substrates. On Ge(111), we found that at the bismuth coverages of 3 MLs and 5 MLs the topmost 2MLs of Bi atoms form a buckled honeycomb structures and were hoped to exhibit the topological non-trivial phase. However, in the band structure calculations, the beneath Bi atoms play an important role in p-type doping to the topmost 2D topological insulator. The p-type doping results in shifts of Fermi level and changes of parity at the time-reversal symmetry points of the system, thus the topological non-trivial characteristic is broken. In the contrast, at 3 ML and 5 ML the buckled bismuth bilayer was unable to form on Si(111) substructure due to the a larger compressive strain compared to Ge(111). |
目次 Table of Contents |
論文審定書 i 摘要 ii Abstract iii 圖 次 vi 表 次 xi Chapter 1 Introduction 1 Chapter 2 Theory and computational methods 4 2.1 Density functional theory (DFT) 4 2.1.1 Thomas-Fermi model 4 2.1.2 The Hohenberg-Kohn theorem 5 2.1.3 The Kohn-Sham equation with local spin density approximation (LSDA) and generalized gradient approximation (GGA) 7 2.1.4 Spin–orbit interaction 10 2.2 The pseudopotential method 12 2.2.1 Norm-conserving pseudopotential 12 2.2.2 Projector augmented waves (PAW) 14 2.3 Hellmann-Feynman theorem 16 2.4 Rashba effect 17 2.4 Computational details 21 Chapter 3 Result and discussion I: Atomic structures and stabilit 23 3.1 The phases of pure Bi 23 3.2 Atomic structures of Bi on Ge(111)-( )R30° 25 3.2.1 1/3ML of Bi 25 3.2.2 2/3ML of Bi 26 3.2.3 1ML of Bi 27 3.2.4 4/3ML of Bi 28 3.2.5 5/3ML of Bi 29 3.2.6 2ML of Bi 30 3.2.7 3ML,4ML and 5ML of Bi 31 3.3 Atomic structures of Bi on Si(111)-( )R30° 32 3.3.1 1/3ML of Bi 32 3.3.2 2/3ML of Bi 33 3.3.3 1ML of Bi 35 3.3.4 4/3ML of Bi 36 3.3.5 5/3ML of Bi 37 3.3.6 2ML of Bi 39 3.3.7 3ML,4ML and 5ML of Bi 40 3.4 Formation energy 42 Chapter 4 Result and Discussions II: Electronic Structures 46 4.1 The band structure of Bi on Ge(111)-( ) 47 4.2 The band structure of Bi on Si(111)-( ) 56 Chapter 5 Conclusions 67 Bibliography 69 |
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