博碩士論文 103222023 詳細資訊




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姓名 古承偉(Cheng-Wei Gu)  查詢紙本館藏   畢業系所 物理學系
論文名稱
(Combined first-principles and tight-binding Hamiltonian study of Fe-MgO-Fe magnetic tunnel junctions)
檔案 [Endnote RIS 格式]    [Bibtex 格式]    至系統瀏覽論文 (2018-7-31以後開放)
摘要(中) 近年來隨著科技元件的發展,具有非揮發性 (nonvolatility)、快速讀寫、低功耗及高元件整合密度的磁電阻式隨機存取記憶 (magnetoresistive random access memory,MRAM) 已經被廣泛的使用。另一方面,隨著長晶技術的成長,以氧化物作為穿隧阻絕層的應用已經能達到較高的穿隧磁阻值 (Tunneling Magnetoresistance, TMR).
在理論模擬上,我們分別選用氧化鎂與鐵做為阻絕層與電極,並在鐵的 (001) 方向接上氧化鎂 (001) 形成鐵/氧化鎂的超晶格(superlattice) 。利用第一原理的方法 (First Principles) 計算其最低能量的原子位置。鐵/氧化鎂的超晶格可以被拆成兩部分並作為重建鐵/氧化鎂/鐵磁穿隧接合(Fe/MgO/Fe MTJs)中的接面(interfaces)。在塊材(Bulk)分析上,我們計算鐵與氧化鎂的能帶結構(band structure),並歸納出四種軌道對稱性:∆1, ∆2, ∆2′與∆5。位能分析法確定了至少需要七層的氧化鎂才能夠降低邊界效應的影響,此時最中間的絕緣層能視為塊材結構。七層結構的穿隧特性則透過非平衡態的格林函數法(Non-equilibrium Green’s function method)做計算。結果發現平行磁矩組態時,以氧化鎂作為穿隧接合中的阻絕層時可以得到很低的磁阻率 (Magnetoresistance, MR);電子透射係數(transmission spectra) 的分析顯示自旋向上電子在費米能 (Fermi energy) 附近存在∆1傳輸通道。如果磁矩呈現反平行時,導致自旋向上與自旋向下的電子傳輸通道的對稱性消失與較高的MR值。投影態密度(Projected density of states)的分析說明自旋注入現象(Spin injection phenomenon)主要是由對稱性∆1而來。結合氧化鎂的複數能帶分析(Complex band structure analysis),更推論其它對稱性如∆2, ∆2′與∆5因擁有較大的衰減率(decay rates),故∆1對稱性在平行組態傳輸上扮演著相當重要的角色。
最後,我們也探討了如何利用少層氧化鎂結構預測多層氧化鎂結構時的傳輸特性。方法上,係藉由重組七層氧化鎂結構與塊材絕緣體的哈密噸,能夠精準的預測九層結構的傳輸特性,而十一層結構的傳輸特性亦可透過類似的重組方式進行計算。而此方法有很大的機會在未來能被應用於計算量龐大或大系統結構中,進而改善第一原理計算耗時的缺點。
摘要(英) In recent years, the nonvolatile, fast reading and writing and low-power consuming magnetoresistive random access memory (MRAM) has been widely used. Based on the development of the oxide-based heteroepitaxy in magnetic tunnel junctions (MTJs), the high tunneling magnetoresistance (TMR) ratio can be achieved.
Theoretically, we adopt magnesium oxide (MgO) and iron (Fe) as our insulator and electrodes, respectively, and the fcc MgO (001) and the bcc Fe (001) are linked together to form the Fe/MgO superlattice, which can be optimized and further used to reconstruct the Fe/MgO interfaces in Fe/MgO/Fe MTJs.
The first-principles calculation is first employed to analyze the band structures of Fe and MgO bulk materials, which energy bands near the Fermi energy (EF) can be classified into several groups in terms of different orbital symmetries : ∆1, ∆2, ∆2′ and ∆5. In addition, our potential analysis confirms that the number of left (right) Fe buffer layers cannot be smaller than four (five), and at least seven layers of MgO are required to avoid the strong charge transfer at Fe/MgO interface. The NEGF-DFT+LDA calculation is further employed to obtain the spin-polarized transmission spectra and the projected density of states (PDOS) for Fe/MgO/Fe MTJs in parallel (PC) and anti-parallel (APC) magnetic configurations. We combine spin-polarized transmission and PDOS’s to demonstrate that the majority electrons with symmetric ∆1 can easily tunnel through junction in PC case and then leads to lower electric resistivity. In contrast, higher electric resistivity in APC is observed because of the destruction of Bloch states without symmetric ∆1. Thus, the highly distinct two electric resistivity between PC and APC cases gives rise to a high predicted TMR ratio over 4000% for seven-layer device.
Finally, we employ the NEGF-DFT calcuation to provide a novel method to rebuild the Hamiltonian of Fe/MgO/Fe junctions with nine- and eleven-layers of central MgO, simply via the combination of bulk MgO and seven-layer device, to efficiently predict the transport properties in multi-layer MTJs and even to avoid the time consuming issue of first-principles calculation in large and complex systems.
關鍵字(中) ★ 第一原理
★ 巨磁阻
★ 穿隧磁阻
★ 密度泛函
★ 非平衡態格林函數
關鍵字(英) ★ Fe-MgO-Fe
★ first-principles
★ tight-binding
★ magnetic tunnel junctions
論文目次 Chapter 1 Introduction.........................................................................1
Chapter 2 Theory...................................................................................5
2.1 Density Function Theory.........................................................5
2.1.1 Born-Oppenheimer Approximation..........................5
2.1.2 Hartree-Fock Approximation....................................6
2.1.3 The Hohenberg-Kohn Theorem................................8
2.1.4 The Kohn-Sham Equation.......................................10
2.1.5 Exchange-Correlation Energy Functionals............13
 Local Density Approximation (LDA)...................13
 Generalized Gradient Approximation (GGA).....14
2.2 Pseudopotential Method for DFT calculation.....................15
2.2.1 Bloch’s Theorem and Cutoff Energy...................15
2.2.2 Pseudopotentials.......................................................16
2.3 Non-Equilibrium Green’s Function Method.......................18
2.3.1 Self-Consistent in NEGF-DFT Calculation............18
2.3.2 Tight-Binding Model................................................21
 Tight-Binding Hamiltonain based on LCAO.......22
 Green’s function and Self-energy..........................24
 K-resolved transmission and Density of States....27
Chapter 3 Computational Details.......................................................29
3.1 Structural Geometry.....................................................29
3.2 Parameters for Structural Relaxation.........................31
3.3 Parameters for Spin Transport Property..................33
Chapter 4 Results and Discussions.....................................................35
4.1 Bulk Properties for Iron and Magnesium Oxide................35
4.1.1 Structural Relaxation...............................................35
4.1.2 Electronic Properties................................................36
4.2 Spin Transport in Fe/MgO/Fe MTJs.................43
4.2.1 Potential Energy Analysis........................................43
4.2.2 Density of States Aanalysis......................................47
4.2.3 Transmission and Conductance..............................51
4.3 Tight-binding Hamiltonian Investigation............................54
4.3.1 Concepts of Hamiltonian Recombination..............54
4.3.2 Determination of Hamiltonian Parameters..........58
 Hamiltonian from 7- to 9- Layer Device...............58
 Hamiltonian for 11-Layer Device..........................61
Chapter 5 Summary............................................................................65
References................................................................................................67
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指導教授 唐毓慧(Yu-Hui Tang) 審核日期 2016-7-20
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