Responsive image
博碩士論文 etd-0623113-160745 詳細資訊
Title page for etd-0623113-160745
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)
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
83
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
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
統計
Statistics
本論文已被瀏覽 5730 次,被下載 568
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
參考文獻 References
[1] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[2] B. A. Bernevig, T. L. Hughes and S. C. Zhang, Science 314, 1757 (2006).
[3] Z. Liu, C. X. Liu, Y. S. Wu, W. H. Duan, F. Liu and J. Wu, Phys. Rev. Lett. 107, 136805 (2011).
[4] Z.Q. Huang, F. C. Chuang, C. H. Hsu, Y. T. Liu, H. R. Chang, H. Lin and A. Bansil, Nontrivial topological electronic structures in single Bi(111) bilayer on substrates : A first-principles study, submitted to Phys. Rev. B.
[5] F.C. Chuang, C. H. Hsu, C. Y. Chen, Z. Q. Huang, V. Ozolins, H. Lin and A. Bansil, Appl. Phys. Lett. 102, 022424 (2013).
[6] Y. Ohtsubo, S. Hatta, M. Iwata, K. Yaji, H. Okuyama and T. Aruga, J. ,Phys.: Condens. Matter 21, 405001 (2009).
[7] M. Kuzmin, P. Laukkanen, R. E. Per¨al¨a, M. A. Tuomi and I. J. V¨ayrynen, Journal of Electron Spectroscopy and Related Phenomena 159,24 (2007).
[8] A. Goriachko , P.V. Melnik, A. Shchyrba, S.P. Kulyk, M.G. Nakhodkin, Surface Science 605, 1771 (2011).
[9] S. Hatta, T. Aruga, Y. Ohtsubo and H. Okuyama, Phys. Rev. B 80, 113309 (2009).
[10] Y. Ohtsubo, S. Hatta, K. Yaji, H. Okuyama, K. Miyamoto, T. Okuda, A. Kimura, H. Namatame, M. Taniguchi, and T. Aruga, Phys. Rev. B 82, 201307 (R) (2010).
[11] E. Frantzeskakis, S. Pons, and M. Grioni, Phys. Rev. B 82, 085440 (2010).
[12] I. Gierz, T. Suzuki, E. Frantzeskakis, S. Pons, S. Ostanin, A. Ernst ,J. Henk, M. Grioni, K. Kern, and C. R. Ast, Phys. Rev. Lett. 103, 046803 (2009).
[13] K. Sakamoto, H. Kakuta, K. Sugawara, K. Miyamoto, A. Kimura, T. Kuzumaki, N. Ueno, E. Annese, J. Fujii, A. Kodama, T. Shishidou, H. Namatame, M. Taniguchi,
T. Sato, T. Takahashi, and T. Oguchi, Phys. Rev. Lett. 103, 156801 (2009).
[14] L. Vitali, M. G. Ramsey, and F. P. Netzer Phys. Rev. B 63, 165320 (2001).
[15] T. M.Schmidt, R. H. Miwa, and G. P. Srivastava, Brazilian Journal of Physics 34 , 629 (2004).
[16] T. Kuzumaki, T. Shirasawa, S. Mizuno, N. Ueno,H. Tochihara and K. Sakamoto, Surface Science 604, 1044 (2010).
[17] Y. A. Bychkov, E. I. Rashba, J. Phys. C: Solid State Phys. 17, 6039 (1984).
[18] D. Stein, K. v. Klitzing and G. Weimann, Phys. Rev. Lett. 51, 130 (1983).
[19] H. L. Stormer, Z. Schlesinger, A. Chang, D. C. Tsui, A C. Gossard and W. Wiegmann, Phys. Rev. Lett. 51, 126 (1983).
[20] M. Nagano, A. Kodama, T. Shishidou and T. Oguchi, J. Phys.: Condens. Matter 21, 064239 (2009).
[21] C. R. Ast, J. Henk, A. Ernst, L. Moreschini, M. C. Falub, D. Pacile, P. Bruno, K. Kern and M. Grioni, Phys. Rev. Lett. 98, 186807 (2007).
[22] Y. S. Dedkov, M. Fonin, U. Ru¨diger and C. Laubschat, Phys. Rev. Lett. 100, 107602 (2008).
[23] A. Varykhalov, J. Sa´nchez-Barriga, A. M. Shikin, C. Biswas, E. Vescovo, A. Rybkin, D. Marchenko and O. Rader, Phys. Rev. Lett. 101, 157601 (2008).
[24] C. H. Hsu, W. H. Lin, V. Ozolins, and F. C. Chuang, Appl. Phys. Lett. 100, 063115 (2012).
[25] L.H. Thomas, Proc. Cambridge Phil. Roy. Soc. 23, 542 (1927).
[26] E. Fermi, Rend. Accad. Naz. Lincei, 6, 602 (1927).
[27] M. Born and J. R. Oppenheimer, Ann. Physik, 84, 457 (1927).
[28] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
[29] D. R. Hamann, M. Schluter, and C. Chiang, Phys. Rev. Lett. 43, 1494 (1979).
[30] B.H. Bransden , C.J. Joachain, Physics of atoms and molecules, Prentice Hall, (2003).
[31] M. Weissbluth, Atoms and Molecules, Academic Press (1978).
[32] P. E. Blochl, Phys. Rev. B. 50, 17953 (1994).
[33] R. P. Feynman, Phys. Rev. 56, 340 (1939).
[34] M. C. Payn, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992).
[35] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990).
[36] G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).
[37] G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996).
[38] J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).
[39] H. J. Monkhorst and J.D. Pack, Phys. Rev. B 13, 5188 (1976).
[40] K. J. Wan, T. Guo, W. K. Ford and J. C. Hermanson, Phys. Rev. B 44, 3471 (1991).
[41] C. Cheng and K. Kunc, Phys. Rev. B 56, 16 (1997).
[42] K. J. Wan, W. K. Ford, G. J. Lapeyre and J. C. Hermanson, Phys. Rev. B 44, 6500, (1991).
[43] R. Shioda, A. Kawazu, A. A. Baski, C. F. Quate and J. Nogami, Phys. Rev. B 48, 4895 (1993).
[44] Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki 58, 486 (1970).
[45] R. M. Brugger, R. B. Bennion, and T. G. Worlton, Phys. Lett. A 24A, 714 (1967).
電子全文 Fulltext
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。
論文使用權限 Thesis access permission:自定論文開放時間 user define
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus: 已公開 available


紙本論文 Printed copies
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。
開放時間 available 已公開 available

QR Code