纳米器件中电子输运的系统分析

发布时间：2018-05-17 22:33

本文选题：纳米器件 + Bloch理论　；参考：《浙江大学》2017年博士论文

【摘要】：随着纳米器件的制备技术日益提高,量子输运的理论研究越来越得到重视。研究纳米体系中的输运可以为我们提供一种微观视角,从而理解纳米器件中的各种特性,为未来各种新的纳米器件的制备提供理论参考。在一个纳米器件中,信息的传播需要依靠传播子,如电子,声子,磁振子,自旋等,其中电子最为常见。在以往的研究中,电流、电导等特性首先得到关注,器件中电子传播的各种细节比如各种模式的信息往往被忽略。所以,我们需要一个可靠又方便的理论工具在来处理纳米体系中的电子输运的细节信息。本文从量子输运体系的基本模型和现有理论出发,分析和研究了格林函数,散射矩阵和Bloch理论,通过将格林函数和Bloch理论相结合,找到了一种普遍适用的模式分析法。该方法可专门用于研究纳米器件中的各种模式的详细信息,也可以作为一种可随时调用的工具出现在其他纳米体系的研究中,用于分析其中的模式信息。文中的主要内容如下:本文首先介绍了一般量子体系的基本模型,阐述了Bloch理论,散射矩阵与格林函数的基本概念。在紧束缚表象下,通过对周期性结构的体系中的Bloch本征模的求解,所得到的Bloch传播矩阵来描述体系内的波函数的传播过程。我们重点研究了复杂体系如耦合矩阵为奇异矩阵和多层结构的情况,扩展了Bloch理论的适用范围,并套用格林函数中的概念,对Bloch波进行了解析延拓,得到了超前和延迟的Bloch本征模。在充分了解Bloch理论的基础上,我们将格林函数与其相结合,用Bloch语言来表述格林函数格林函数理论中的各个量,如表面格林函数,自能,线宽等,最后得出了两种理论的等价性。两种理论中各个量的对应关系也对我们理解这些量的物理意义有很大帮助。在格林函数理论中,Fisher-Lee关系式t=iΓL1/2GΓR1/2可以用于描述模式→模式的输运过程,我们证明ΓΓL/R1/2需要Bloch本征模来定义才能确保其唯一性,说明ΓL/R1/2连接了两种方法。通过格林函数的辅助,Bloch本征模的求解过程也可以大大简化,并绕过复杂的数学算法,得到体系的模式信息,并由Fisher-Lee关系式得到各个模式的输运信息。这个过程称之为模式分析法。模式分析法由于和格林函数的紧密结合使其较之单纯的Bloch理论和模式匹配应用场景更广。本文将模式分析法应用到石墨烯模型中,得到了其中的模式信息,理清了每种模式的传播过程,分析了各种模式对输运的贡献,证明模式分析法准确与方便的特性。此外,本文结合现有的石墨烯场效应管,将其缩小后进行建模,分别讨论了源极、漏极、栅极电压对于该器件的导电性和电流特性的影响,并分析了电子输运模式在其中发挥的作用。由此实现了理论工作和实际器件的结合,为未来小尺寸石墨烯场效应管的开发提供了参考。
[Abstract]:With the increasing development of the fabrication technology of nanodevices, more and more attention has been paid to the theory of quantum transport. The study of transport in nanoscale system can provide a microscopic perspective for us to understand the characteristics of nanodevices and provide a theoretical reference for the preparation of new nanodevices in the future. In a nanoscale device, the propagation of information depends on propagators, such as electrons, phonons, magnetic oscillators, spins and so on, in which electrons are the most common. In previous studies, the characteristics of current and conductance have been paid attention to first, and the details of electron propagation, such as the information of various modes, are often ignored. Therefore, we need a reliable and convenient theoretical tool to handle the details of electron transport in nanosystems. Based on the basic model and existing theory of quantum transport system, Green's function, scattering matrix and Bloch's theory are analyzed and studied in this paper. By combining Green's function and Bloch's theory, a general applicable mode analysis method is found. This method can be used to study the detailed information of various modes in nanodevices, and can also be used as a tool to be used at any time to analyze the mode information in other nanosystems. The main contents of this paper are as follows: firstly, the basic models of general quantum systems are introduced, and the basic concepts of Bloch theory, scattering matrix and Green's function are expounded. Under the tight bound representation, the Bloch propagation matrix is obtained to describe the propagation process of the wave function in the system by solving the Bloch eigenmode in the system with periodic structure. We focus on the case that the coupling matrix is a singular matrix and a multilayer structure. We extend the scope of application of the Bloch theory and apply the concept of Green's function to the analytic continuation of the Bloch wave. The leading and delayed Bloch eigenmodes are obtained. On the basis of fully understanding the Bloch theory, we combine Green's function with it, and use Bloch language to express the various quantities in Green's function theory, such as surface Green's function, self-energy, linewidth, etc. Finally, the equivalence of the two theories is obtained. The corresponding relation of each quantity in the two theories is also of great help to us to understand the physical meaning of these quantities. In Green's function theory, the Fisher-Lee relation TX ~ I 螕 L _ 1 / 2G 螕 R _ 1 / 2 can be used to describe the transport process of the mode L/R1/2. We prove that 螕 -螕 L/R1/2 needs the Bloch eigenmode to be defined to ensure its uniqueness. It is shown that 螕 L/R1/2 is connected by two methods. The solution of the eigenmode of Bloch by Green's function can also be simplified greatly, and the model information of the system can be obtained by bypassing the complicated mathematical algorithm, and the transport information of each mode can be obtained by the Fisher-Lee relation. This process is called pattern analysis. Because of its close combination with Green's function, the pattern analysis method is more widely used than the simple Bloch theory and pattern matching. In this paper, the pattern analysis method is applied to the graphene model, the mode information is obtained, the propagation process of each model is clarified, the contribution of each model to transport is analyzed, and the accuracy and convenience of the mode analysis method are proved. In addition, combined with the existing graphene field effect transistor, the model is modeled after its reduction, and the effects of source, drain and gate voltage on the conductivity and current characteristics of the device are discussed, respectively. The function of electronic transport mode is analyzed. Thus, the combination of theoretical work and practical devices is realized, which provides a reference for the development of small size graphene FET in the future.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TB383.1

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