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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 12 Some basic concepts 72.1 Electrical resistance . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1 Source and scattering . . . . . . . . . . . . . . . . . . . 72.1.2 Incoherent scattering and relaxation time . . . . . . . . 82.1.3 Scattering and available states . . . . . . . . . . . . . . 102.1.4 Conductance electron . . . . . . . . . . . . . . . . . . . 102.2 Spin-dependent scattering . . . . . . . . . . . . . . . . . . . . 112.2.1 Origin of bulk spin-dependent scattering . . . . . . . . 112.2.2 Origin of interfacial spin-dependent scattering . . . . . 142.3 Spin-‡ipping scattering . . . . . . . . . . . . . . . . . . . . . . 172.4 Conservation of spin and two channels . . . . . . . . . . . . . 182.5 Essential ingredients . . . . . . . . . . . . . . . . . . . . . . . 193 GMR and Equivalent Resistor Network Theory 213.1 GMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1.1 De…nition . . . . . . . . . . . . . . . . . . . . . . . . . 213.1.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.3 Asymmetrical spin-dependent scattering . . . . . . . . 233.1.4 Two spin-dependent current channels . . . . . . . . . . 243.1.5 Physical origin of GMR from the simple resistor model 243.2 Equivalent resistor network theory . . . . . . . . . . . . . . . . 263.2.1 An unit cell . . . . . . . . . . . . . . . . . . . . . . . . 263.2.2 Three local resistivities . . . . . . . . . . . . . . . . . . 273.2.3 CIP-GMR . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.4 CPP-GMR . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Advantages and shortcomings . . . . . . . . . . . . . . . . . . 344 Boltzmann transport equation model 374.1 Boltzmann transport equation . . . . . . . . . . . . . . . . . . 374.1.1 Semiclassical approach . . . . . . . . . . . . . . . . . . 374.1.2 Electron distribution . . . . . . . . . . . . . . . . . . . 384.1.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . 394.1.4 Current density . . . . . . . . . . . . . . . . . . . . . . 434.2 Reduced Boltzmann transport equation model . . . . . . . . . 444.3 Spin-independent Boltzmann transport equation model . . . . 474.4 Spin-dependent Boltzmann transport equation model . . . . . 494.4.1 Linear response spin-dependent Boltzmann transportequation in the relaxation time approximation . . . . . 504.4.2 Layered structures . . . . . . . . . . . . . . . . . . . . 514.4.3 Trilayer structures . . . . . . . . . . . . . . . . . . . . 534.4.4 Shortcomings and two di¢ culties . . . . . . . . . . . . 565 E¤ective mean-free-path model 575.1 Novel approach . . . . . . . . . . . . . . . . . . . . . . . . . . 595.1.1 Basic concept . . . . . . . . . . . . . . . . . . . . . . . 595.1.2 E¤ective di¤usive scattering . . . . . . . . . . . . . . . 605.1.3 Equilibrium di¤usion parameter . . . . . . . . . . . . . 615.1.4 Diagrammatical method . . . . . . . . . . . . . . . . . 625.1.5 E¤ective mean free path . . . . . . . . . . . . . . . . . 635.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Validity and examination . . . . . . . . . . . . . . . . . . . . . 655.2.1 Trilayer structures . . . . . . . . . . . . . . . . . . . . 665.2.2 Trilayer structure with simple boundary conditions . . 665.2.3 Trilayer structure with more general boundary conditions 715.2.4 Any multilayer structure . . . . . . . . . . . . . . . . . 795.2.5 Other structures . . . . . . . . . . . . . . . . . . . . . 815.2.6 Structures with various shapes . . . . . . . . . . . . . . 865.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 Conclusion 89A List of Symbols and Abbreviations 93B Publications 99
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