纳米MOSFET迁移率解析模型

从玻尔兹曼方程出发，重新计算了纳米MOSFET沟道内的载流子所服从的分布函数，特别是考虑了纳米MOSFET横向电场和纵向电场之间的相互作用，并且以得到的非平衡状态下的分布函数为基础，考虑载流子寿命和速度的统计分布，给出了纳米MOSFET载流子迁移率的解析表达式.通过与数值模拟结果进行比较和分析，该迁移率解析模型形式简洁、物理概念清晰，且具有相当精度. 关键词： 玻尔兹曼方程 纳米MOSFET 迁移率 沟道有效电场     

Classical Theory of Hot-Electron Transport in Electric and Magnetic Fields

Balance equation approach to the hot-electron transport in electric and magnetic fields is reformulated.The balance equations are re-derived from the Boltzmann equation. A new expression for the distribution function isreported in the present paper. It is homogeneous steady solution of the Boltzmann equation in constant relaxation timeapproximation. It holds when ωocτ < i or ωc < Te. As an example, the mobility of 2D electron gas in the GaAs-AlGaAsheterojunction is computed as a function of electric field and magnetic field.     

Solution of a linearized kinetic model for an ultrarelativistic gas

A linearized model of the Boltzmann equation for a relativistic gas is shown to be reducible, in the ultrarelativistic limit and for (1 + 1)-dimensional problems, to a system of three uncoupled transport equations, one of which is well known. A general method for solving these equations is recalled, with a few new details, and applied to the solution of two boundary value problems. The first of these describes the propagation of an impulsive change in a half space and is shown to give an explicit example of the recently proved result that no signal can propagate with speed larger than the speed of light, according to the relativistic Boltzmann equation. The second problem deals with steady oscillations in a half space and illustrates the meaning of certain recent results concerning the dispersion relation for linear waves in relativistic gas.     

Low-field carrier transport properties in biased bilayer graphene

Based on a semiclassical Boltzmann transport equation in random phase approximation, we develop a theoretical model to understand low-field carrier transport in biased bilayer graphene, which takes into account the charged impurity scattering, acoustic phonon scattering, and surface polar phonon scattering as three main scattering mechanisms. The surface polar optical phonon scattering of carriers in supported bilayer graphene is thoroughly studied using the Rode iteration method. By considering the metal–BLG contact resistance as the only one free fitting parameter, we find that the carrier density dependence of the calculated total conductivity agrees well with that observed in experiment under different temperatures. The conductivity results also suggest that in high carrier density range, the metal–BLG contact resistance can be a significant factor in determining the BLG conductivity at low temperature, and both acoustic phonon scattering and surface polar phonon scattering play important roles at higher temperature, especially for BLG samples with a low doping concentration, which can compete with charged impurity scattering.     

Large energy behavior of the velocity distribution for the hard-sphere gas

The initial-value problem for the Boltzmann-Lorentz equation for hard spheres at zero temperature is shown to be ill defined, the general solution depending on an arbitrary function. The uniqueness of the solution can be obtained by imposing the conservation of the number of particles (Carleman's type of condition does not suffice). The linearized Boltzmann equation for hard spheres is then analyzed, as it occurs in Enskog's method for calculating transport coefficients. It is demonstrated that in the case of viscosity and diffusion it is necessary to add supplementary conditions to obtain the uniqueness of the solution. The nonuniform character of Enskog's expansion and violation of positivity in the large velocity region are exhibited.     

锐钛矿和金红石二氧化钛中光生载流子的超快动力学：电声相互作用研究

本文结合玻尔兹曼输运方程和电声散射速率计算研究锐钛矿和金红石二氧化钛中光生载流子的超快动力学过程. 其中,动力学模拟所需的结构参数均通过第一性原理计算获得. 结果表明,由于存在强Fr?hlich型电声耦合,纵光学声子模对两个晶相的能量弛豫过程均有十分显著的影响,但是两个晶相的弛豫机理却表现出明显的差异. 对于单条导带内的弛豫过程,锐钛矿和金红石的能量弛豫时间分别为24.0 fs和11.8 fs,前者约为后者的二倍. 这一差异来源于两个晶相中不同的电子扩散分布以及不同的声学模散射贡献. 对于涉及多条导带的弛豫过程,预测的锐钛矿和金红石的总体弛豫时间分别为47 fs和57 fs,其相对大小与单条导带的情况相反. 分析表明金红石相弛豫较慢是因为存在多个速率控制步骤. 这些发现为调控电子动力学以及设计高效的二氧化钛器件提供了有价值的信息.     

The unique carrier mobility of Janus MoSSe/GaN heterostructures

Heterostructure is an effective approach in modulating the physical and chemical behavior of materials. Here, the first-principles calculations were carried out to explore the structural, electronic, and carrier mobility properties of Janus MoSSe/GaN heterostructures. This heterostructure exhibits a superior high carrier mobility of 281.28 cm²·V⁻¹·s⁻¹ for electron carrier and 3951.2 cm²·V⁻¹·s⁻¹ for hole carrier. Particularly, the magnitude of the carrier mobility can be further tuned by Janus structure and stacking modes of the heterostructure. It is revealed that the equivalent mass and elastic moduli strongly affect the carrier mobility of the heterostructure, while the deformation potential contributes to the different carrier mobility for electron and hole of the heterostructure. These results suggest that the Janus MoSSe/GaN heterostructures have many potential applications for the unique carrier mobility.     

The linearized Boltzmann equation: a concise and accurate solution of the temperature-jump problem

Polynomial expansion procedures, along with an analytical discrete-ordinates method, are used to solve the temperature-jump problem based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, the temperature and density perturbations and the temperature-jump coefficient are obtained (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented for general values of the accommodation coefficient to yield numerical results that can be considered a new standard of reference.     

Quasiclassical mobility for extrinsic semiconductors

A quasiclassical formulation for mobility in extrinsic semiconductors is presented based on scattering from ionized impurity atoms. Quantum theory enters the otherwise classical Chapman-Enskog expansion of the Boltzmann equation through incorporation of the Thomas-Fermi interaction potential together with the Bom approximation for evaluation of scattering integrals. The following expression results for mobility μ_i, (cgs):

$\text{μ}{}_{\mathrm{i}}\text{3}\text{2}\text{?}{}^2\text{n}{}_{\mathrm{s}}\text{e}{}^3\text{m}{}^1\text{2}\text{2}\text{k}{}_{\mathrm{B}}\text{T}\text{2φ}\text{3}\text{2}\text{1}\text{f(γ)}$

,

$\text{f(γ)=[(1+γ)e}{}^{\mathrm{\gamma }}\text{E}{}_1\text{(γ)?1]}$

, where n_s is impurity concentration, m¹ is effective mass, E₁(γ) is the exponential integral, ? is dielectric constant and γ is dimensionless Thomas-Fermi energy. The structure of the dimensional factor in the preceding expression for μ_i agrees with previous expressions for this parameter.     

Solution of the BGK model kinetic equation for very hard particle interaction

We study the Bhatnagar-Gross-Krook model kinetic equation with a velocity-dependent collision frequency. We derive the conditions that must be verified in order to keep the main physical properties of the Boltzmann equation, i.e.,H-theorem and conservation laws. The particular case of the so-called VHP interaction is considered, and the resulting kinetic equation is solved for a homogeneous and isotropic gas. Overpopulation phenomena are observed and analyzed for some kinds of initial conditions. The results are compared, where possible, with the exact solution of the Boltzmann equation.     

低温下二硫化钼电子迁移率研究

二硫化钼(MoS₂)是已知的二维半导体材料中光电性能最优秀的材料之一. 单原子层厚的MoS₂是禁带宽度为1.8 eV 的二维直接带隙半导体材料, 可以用来发展新型的纳米电子器件和光电功能器件. 本论文利用玻尔兹曼平衡方程输运理论研究低温时MoS₂系统的电输运性质, 计算得到了MoS₂电子迁移率的解析表达式. 研究发现, 低温时MoS₂ 的迁移率与衬底材料的介电常数的平方成正比; 与系统的电子浓度对带电杂质的浓度的比率n_e/n_i 成线性关系. 因此, 选用介电常数高的衬底材料, 适当提高MoS₂系统的载流子浓度, 同时降低杂质的浓度, 可以有效提高MoS₂系统的迁移率. 研究结果为探索以MoS₂为基础的新型纳米光电器件的研究和实际应用提供了理论依据. 关键词： 二硫化钼 迁移率 电输运 平衡方程     

A random discrete velocity model and approximation of the Boltzmann equation

An approximation procedure for the Boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed. In a suitable limit, the procedure is shown to converge to the time-discretized and spatially homogeneous Boltzmann equation.     

Ac response of a coupled double quantum dot

The effect of phase-breaking process on the ac response of a coupled double quantum dot is studied in this paper based on the nonequilibrium Green function formalism. A general expression is derived for the ac current in the presence of electron--phonon interaction. The ac conductance is numerically computed and the results are compared with those in [Anatram M P and Datta S 1995 Phys. Rev. B 51 7632]. Our results reveal that the inter-dot electron tunnelling interplays with that between dots and electron reservoirs, and contributes prominently to the ac current when inter-dot tunnelling coupling is much larger than the tunnelling coupling between dots and electron reservoirs. In addition, the phase-breaking process is found to have a significant effect on the ac transport through the coupled double dot.     

An Example of Nonuniqueness for Solutions to the Homogeneous Boltzmann Equation

The paper deals with the spatially homogeneous Boltzmann equation for hard potentials. An example is given which shows that, even though it is known that there is only one solution that conserves energy, there may be other solutions for which the energy is increasing; uniqueness holds if and only if energy is assumed to be conserved.     

Thickness dependence of surface morphology and charge carrier mobility in organic field-effect transistors

With the aim of understanding the relationships between organic small molecule field-effect transistors (FETs) and organic conjugated polymer FETs, we investigate the thickness dependence of surface morphology and charge carrier mobility in pentacene and regioregular poly (3-hexylthiophene) (RR-P3HT) field-effect transistors. On the basis of the results of surface morphologies and electrical properties, we presume that the charge carrier mobility is largely related to the morphology of the organic active layer. We observe that the change trends of the surface morphologies (average size and average roughness) of pentacene and RR-P3HT thin films are mutually opposite, as the thickness of the organic layer increases. Further, we demonstrate that the change trends of the field-effect mobilities of pentacene and RR-P3HT FETs are also opposite to each other, as the thickness of the organic layer increases within its limit.     

多约束纳米结构的声子热导率模型研究

纳米技术的快速发展使得对微纳尺度导热机理的深入研究变得至关重要. 理论和实验都表明, 在纳米尺度下声子热导率将表现出尺寸效应. 基于声子玻尔兹曼方程和修正声子平均自由程的方法得到了多约束纳米结构的声子热导率模型, 可以描述多个几何约束共同作用下热导率的尺寸效应. 不同几何约束对声子输运的限制作用可以分开计算, 总体影响则通过马西森定则进行耦合. 对于热流方向的约束, 采用扩散近似的方法求解声子玻尔兹曼方程; 对于侧面边界约束, 采用修正平均自由程的方法计算边界散射对热导率的影响. 得到的模型能够预测纳米薄膜(法向和面向)及有限长度方形纳米线的热导率随相应特征尺寸的变化. 与蒙特卡罗模拟及硅纳米结构热导率实验值的对比验证了模型的正确性.     

耦合不可压流场输运方程的格子Boltzmann方法研究

基于格子Boltzmann方法,提出了求解耦合不可压缩流场输运方程的一种改进数值方法. 该方法使用格子Boltzmann方法求解流场方程,并根据流场格子模型的密度分布函数构建了输运方程的二阶离散格式. 通过二维平板通道流场输运系统验证了该方法的有效性.数值结果表明,该方法可以有效地减少计算过程中出现的非物理耗散, 并克服了传统模型所需巨大存储量的缺点.     

Theoretical insight into the carrier mobility anisotropy of hole transport material Spiro-OMeTAD

All-solid-state organic-inorganic halide perovskite solar cells (PSCs) have attracted wide attention due to the rapid progress of power conversion efficiency in recent years. Hole transport material (HTM) in PSCs plays the role of extracting and transporting photo-excited holes. Anisotropy of carrier mobility is one important property for semiconductors, however, which still remains unclear for the dominant HTM spiro-OMeTAD used in PSCs. Based on Density Functional Theory (DFT) and Marcus theory, we for the first time conducted investigations on the anisotropy of carrier mobility along representative crystal planes of spiro-OMeTAD by recombination energy λ and electronic coupling integral V. Results indicate that the holes and electrons show transport orientations consistency parallel to the (010), (101) and (111) crystal planes while inconsistency was found parallel to (100), (110), (011) and (001) crystal planes (with an angle ranged from 40° to 70° between the hole and electron transport directions). Our work embodies the theoretical significance of controllable and oriented fabrication of HTM in PSCs.     

Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices

A model for the simulation of the electron energy distribution in nanoscale metal–oxide–semiconductor field-effect transistor (MOSFET) devices, using a kinetic simulation technique, is implemented. The convective scheme (CS), a method of characteristics, is an accurate method of solving the Boltzmann transport equation, a nonlinear integrodifferential equation, for the distribution of electrons in a MOSFET device. The method is used to find probabilities for use in an iterative scheme which iterates to find collision rates in cells. The CS is also a novel approach to 2D semiconductor device simulation. The CS has been extended to handle boundary conditions in 2D as well as to calculation of polygon overlap for polygons of more than three sides. Electron energy distributions in the channel of a MOSFET are presented.     

Approximation of the Boltzmann equation by discrete velocity models

Two convergence results related to the approximation of the Boltzmann equation by discrete velocity models are presented. First we construct a sequence of deterministic discrete velocity models and prove convergence (as the number of discrete velocities tends to infinity) of their solutions to the solution of a spatially homogeneous Boltzmann equation. Second we introduce a sequence of Markov jump processes (interpreted as random discrete velocity models) and prove convergence (as the intensity of jumps tends to infinity) of these processes to the solution of a deterministic discrete velocity model.