超小型半导体器件的设计和仿真

发布时间：2018-02-10 13:20

本文关键词： 输运过程玻尔兹曼方程流体力学方程魏格纳方程矩展开累积展开 Maple仿真　出处：《广东工业大学》2015年硕士论文　论文类型：学位论文

【摘要】：本课题对纳米半导体器件仿真输运理论进行研究,以传统、成熟的扩散-漂移为基础的输运理论已经无法满足目前纳米半导体器件开发和仿真,急需通用、准确、计算效率高的包含非平衡载流子输运理论。流体力学模型仿真方法比传统的扩散一漂移方法增加了高阶偏微分方程,可以独立描述器件小型化所带来的载流子温度、热电子效应和部分非平衡态效应。本文从波尔兹曼传输方程入手,对玻尔兹曼传输方程进行矩展开到前三阶,将其转化为粒子流守恒、动量守恒和能量守恒三个偏微分方程组,从而推导出流体力学方程,该模型适用于非抛物线能带结构。并详细推导出通用流体力学模型(托马斯模型)。引入魏格纳方程,结合量子力学薛定谔方程,对魏格纳方程进行矩展开,得出量子流体力学模型。该模型完全考虑量子机械效应,弥补了半经典玻尔兹曼方程所忽视的散射元散射所带来的量子效应。同时,对量子能量传输模型进行简化,并利用中心有限差分方法对该模型进行数值离散,确定了电子密度和温度的关系。接着引入累积展开,以带漂移的麦克斯韦分布为例,检查特征函数累积分布的有效性。在阐明累积展开相对于矩展开的优势后,得出累与矩的关系表达式,同时对波尔兹曼方程进行傅里叶变换并提取特征函数,得到关于累的偏微分方程组。纳米器件中的波尔兹曼方程的碰撞项主要由声子(晶格)散射、界面散射和电离杂质散射组成。本文利用量子力学费米方法结合适用的载流子能带结构模型,研究光学声子(Optic Phonon)、声学声子(Acoustic Phonon)、界面和电离杂质微观散射率,将微观量子散射模型代替维象的迁移率模型和弛豫时间近似。利用累积展开,对碰撞项进行傅里叶变换并提取特征函数后得到前三阶碰撞累。接着,借助量子力学微扰知识,以光学声子为例,得出碰撞项具体表达式,摆脱了目前非平衡输运理论中的不准确的弛豫时间近似。最后,利用Maple数学仿真软件,分别对分布函数接近高斯分布时的系统特征函数、矩展开量与累积展开量关系表达式以及对玻尔兹曼方程进行傅里叶变换后提取特征函数进行模拟,验证结果的准确性。
[Abstract]:In this paper, the simulation transport theory of nanoscale semiconductor devices is studied. The transport theory based on traditional and mature diffusion-drift can not meet the current development and simulation of nanoscale semiconductor devices, so it is urgently needed to be universal and accurate. The computational efficiency includes the theory of non-equilibrium carrier transport. Compared with the traditional diffusion-drift method, the numerical simulation of fluid dynamics model increases the higher order partial differential equation, and can independently describe the carrier temperature brought by the miniaturization of the device. Hot electron effect and partial nonequilibrium state effect. In this paper, the Boltzmann transport equation is expanded to the first three order from the Boltzmann transport equation, which is transformed into three partial differential equations: particle flow conservation, momentum conservation and energy conservation. Thus, the hydrodynamic equation is derived, which is suitable for the non-parabolic band structure. A general hydrodynamic model (Thomas model) is derived in detail. The Wigner equation is introduced and the Schrodinger equation of quantum mechanics is combined. The quantum hydrodynamics model is obtained by moment expansion of the Wigner equation, which fully considers the quantum mechanical effect, which makes up for the quantum effect caused by scattering of scattering elements neglected by the semi-classical Boltzmann equation. At the same time, The quantum energy transfer model is simplified, the central finite difference method is used to discretize the model, and the relationship between electron density and temperature is determined. Then, the cumulative expansion is introduced, and the Maxwell distribution with drift is taken as an example. Check the validity of cumulative distribution of eigenfunction. After clarifying the advantage of cumulative expansion over moment expansion, the relation expression of cumulant and moment is obtained. At the same time, the Fourier transform of Boltzmann equation is carried out and the characteristic function is extracted. The collision term of the Boltzmann equation in nanoscale devices is mainly scattered by phonons (lattice). The composition of interface scattering and ionizing impurity scattering. In this paper, using the Fermi method of quantum mechanics combined with the applicable carrier band structure model, we study the optical phonon Optic Phonon, acoustic phonon acoustic phonon, the microscopic scattering rate of interface and ionization impurity. The microscopic quantum scattering model is used instead of the dimensional mobility model and relaxation time approximation. By using the cumulative expansion, the collision term is transformed by Fourier transform and the characteristic function is extracted to obtain the first three order collision tireds. Then, with the help of quantum mechanical perturbation knowledge, Taking the optical phonon as an example, the concrete expression of the collision term is obtained, which gets rid of the inaccurate relaxation time approximation in the current nonequilibrium transport theory. Finally, the Maple mathematical simulation software is used. The characteristic functions of the distribution function close to Gao Si's distribution, the expression of the relationship between the moment expansion and the cumulative expansion, and the feature function extracted from Boltzmann equation after Fourier transform are simulated, respectively, to verify the accuracy of the results.
【学位授予单位】：广东工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN303

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