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研究生:陳穗斌
研究生(外文):Sui-Pin Chen
論文名稱:自旋相關電子傳輸研究之等效平均自由徑模型
論文名稱(外文):Semiclassical Approach to Studying Spin-dependent Electron Transport: Effective Mean-free-path Model
指導教授:張慶瑞
指導教授(外文):Chang-Ray Chang
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:103
中文關鍵詞:散射電子傳輸自旋等效平均自由徑
外文關鍵詞:effective mean free pathelectron transportdiffusive scatteringspin
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We have developed a novel model in order to study the transport electron in various structures with realistic boundary conditions. The effective mean free path is the main physical quantity used to specify the electron transport in the system; therefore, this model is called the effective mean-free-path model. This model is based on the assumption that the difference between the effective mean free path and the original mean free path is completely attributed to all e¤ective diffusive scatterings in system. Moreover, the general solution for the electron distribution in an applied electric field is related to the effective mean free path, and the undetermined coeffcient in the general solution for the electron distribution is associated with all effective diffusive scatterings. Furthermore, we provide a diagrammatical method to determine all effective diffusive scatterings associated with the effective mean free path and with the solution for the electron distribution. This diagrammatical method has clear physical interpretations and can be used to determine the electron transport in the analytical convergent form. All solutions for the electron distributions obtained from the effective mean-free-path model can be proven to be equivalent to those derived by use of solving the complicated coupled equations from the linear response Boltzmann transport equation in the relaxation time approximation with the given boundary conditions.
1 Introduction 1
2 Some basic concepts 7
2.1 Electrical resistance . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Source and scattering . . . . . . . . . . . . . . . . . . . 7
2.1.2 Incoherent scattering and relaxation time . . . . . . . . 8
2.1.3 Scattering and available states . . . . . . . . . . . . . . 10
2.1.4 Conductance electron . . . . . . . . . . . . . . . . . . . 10
2.2 Spin-dependent scattering . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Origin of bulk spin-dependent scattering . . . . . . . . 11
2.2.2 Origin of interfacial spin-dependent scattering . . . . . 14
2.3 Spin-‡ipping scattering . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Conservation of spin and two channels . . . . . . . . . . . . . 18
2.5 Essential ingredients . . . . . . . . . . . . . . . . . . . . . . . 19
3 GMR and Equivalent Resistor Network Theory 21
3.1 GMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 De…nition . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.3 Asymmetrical spin-dependent scattering . . . . . . . . 23
3.1.4 Two spin-dependent current channels . . . . . . . . . . 24
3.1.5 Physical origin of GMR from the simple resistor model 24
3.2 Equivalent resistor network theory . . . . . . . . . . . . . . . . 26
3.2.1 An unit cell . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Three local resistivities . . . . . . . . . . . . . . . . . . 27
3.2.3 CIP-GMR . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.4 CPP-GMR . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Advantages and shortcomings . . . . . . . . . . . . . . . . . . 34
4 Boltzmann transport equation model 37
4.1 Boltzmann transport equation . . . . . . . . . . . . . . . . . . 37
4.1.1 Semiclassical approach . . . . . . . . . . . . . . . . . . 37
4.1.2 Electron distribution . . . . . . . . . . . . . . . . . . . 38
4.1.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.4 Current density . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Reduced Boltzmann transport equation model . . . . . . . . . 44
4.3 Spin-independent Boltzmann transport equation model . . . . 47
4.4 Spin-dependent Boltzmann transport equation model . . . . . 49
4.4.1 Linear response spin-dependent Boltzmann transport
equation in the relaxation time approximation . . . . . 50
4.4.2 Layered structures . . . . . . . . . . . . . . . . . . . . 51
4.4.3 Trilayer structures . . . . . . . . . . . . . . . . . . . . 53
4.4.4 Shortcomings and two di¢ culties . . . . . . . . . . . . 56
5 E¤ective mean-free-path model 57
5.1 Novel approach . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1.1 Basic concept . . . . . . . . . . . . . . . . . . . . . . . 59
5.1.2 E¤ective di¤usive scattering . . . . . . . . . . . . . . . 60
5.1.3 Equilibrium di¤usion parameter . . . . . . . . . . . . . 61
5.1.4 Diagrammatical method . . . . . . . . . . . . . . . . . 62
5.1.5 E¤ective mean free path . . . . . . . . . . . . . . . . . 63
5.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Validity and examination . . . . . . . . . . . . . . . . . . . . . 65
5.2.1 Trilayer structures . . . . . . . . . . . . . . . . . . . . 66
5.2.2 Trilayer structure with simple boundary conditions . . 66
5.2.3 Trilayer structure with more general boundary conditions 71
5.2.4 Any multilayer structure . . . . . . . . . . . . . . . . . 79
5.2.5 Other structures . . . . . . . . . . . . . . . . . . . . . 81
5.2.6 Structures with various shapes . . . . . . . . . . . . . . 86
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6 Conclusion 89
A List of Symbols and Abbreviations 93
B Publications 99
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