自旋电子学作为一门蓬勃发展的学科，以其很强的实用性和丰富的物理内涵，吸引了全世界众多科学工作者的研究兴趣。随着学科自身的研究边界不断发展与扩大，衍生出众多子学科。如今各类研究中的材料制备都进入纳米尺度。在金属薄膜中，许多物理特性与在金属块体中相比有很大的差异，这是因为出现了量子限制效应。常用的经典粒子的准弹道输运理论适用性受限，许多重要的物理现象和材料性质无法单纯地用经典理论来阐释，需要量子理论的支持。我们需要找到一个经济合理的描述工具兼具衔接宏观和微观物理的能力。基于这样的研究需求，半经典的玻尔兹曼方程进入了我们的研究视野。玻尔兹曼方程作为一种半经典的描述方式，兼具量子性和物理图像相对直观的特点。研究对象的尺寸范围可从超薄薄膜到较厚的块体。本论文主要研究金属薄膜中玻尔兹曼输运方程的数值解法,对传统玻尔兹曼方程进行了量子修正、自旋扩展和数值离散方法等方面的创新，发展数值求解玻尔兹曼方程的程序，针对不同物理问题做了相关的数值模拟研究工作。 本论文在数值求解玻尔兹曼方程的解法层面探索的具体工作内容如下：（1）详细地展示基于奇异矩阵求解技术的半解析半数值的本征根解法的细节过程和解的结构。（2）发展了可完全数值求解的玻尔兹曼方程的离散模型结构与解法。（3）对玻尔兹曼方程在薄膜中的界面散射进行量子修正和自旋扩展，并引入外禀自旋霍尔效应和界面Rashba效应等描述功能，对基本解法和结构又做了相应的补充和调整，进一步增强了玻尔兹曼方程的描述能力。（4）综合采用上述理论解法上的研究，我们编写了两套分别基于本征根解法和离散解法的程序，作为研究薄膜中的玻尔兹曼方程的求解工具，而且，这两套程序在处理相同的物理问题时，数值计算结果是一致的。 本论文在数值模拟方面的主要结果如下：（1）用玻尔兹曼方程数值计算普通金属薄膜中的输运，求解得到薄膜体内的分布函数及电流密度的分布规律，验证我们建立的玻尔兹曼方程两套程序的正确性。（2）系统研究取自不同实验的Cu薄膜电阻率随膜厚度变化的规律，对大量不同生长方式获得的Cu薄膜进行了很好地拟合。（3）通过玻尔兹曼方程的数值计算，探究金属薄膜的霍尔电阻率与纵向电阻率的标度关系。（4）计算具有体自旋霍尔效应的金属薄膜的自旋流分布和电阻率对磁矩的角度依赖关系，结果与相关理论分析是一致的。（5）研究Cu薄膜中界面Rashba自旋轨道耦合磁电阻效应，并与实验的测量值比较，获得了很好的拟合结果。

Spintronics nowadays as a thriving discipline with its strong practicality and abundant physical meaning attracts intensive attentions all around the world. With the evolution of this discipline, different branches quickly establish and develop as its natural growth point. As we know, many material preparations have stepped into the nanoscale. In the metallic thin films, the physical properties, such as resistivity, behave very differently from that in bulk due to quantum confinement effect. Classical ballistic transport description power encounters great challenges from it. Many new phenomenon and material properties cannot be sufficiently interpreted through classical theoretical tools. The support of quantum theory is needed. What we desire is an economical and reasonable method to well describe both macro world and micro world. Based on this research requirement, we choose Boltzmann equation as our research tool. The Boltzmann method is a semi-classical description applied in the thickness range from ultrathin films to bulk. In this dissertation, the numerical solutions for Boltzmann transport equation in metallic thin films are studied. Besides quantum correction, spin dimension extension and numerical discrete methods, we investigate different systems through Boltzmann equation. This specific contributions from numerical algorithm to Boltzmann equations are as follows: (1) a singular value decomposition technique is introduced here for a semi-analytical and semi-numerical method to Boltzmann equation elaborately; (2) a set of full numerical discrete method of solving Boltzmann equation is constructed and developed; (3) through implanting the quantum correction, spin extention, extrinsic bulk spin Hall effect and interfacial Rashba effect into the Boltzmann equation, the basic solutions have been improved and the Boltzmann description power has been enhanced; (4) two reliable and efficient programs have been coded according to above two numerical methods. And the two programs will have same outcomes when addressing the same physical conditions. The specific investigation and calculation results of numerical simulation are as follows: (1) by calculating the distribution function and current density distribution in thin metallic film, we verify the validity of our programs; (2) we investigate the thickness dependent resistivity data from various experiments of thin copper film resistivity systematically; (3)we verify the proper scaling relationship in the quantum confinement thin films through numerical calculations; (4)we study the distribution of spin current density and angle dependent resistivity in the metallic thin film with spin-orbit coupling; (5) we study the interfacial spin-orbit magnetoresistance in ultra-thin copper films, and obtain good fitting results with the experiment.