半导体模型的间断体积元方法
发布时间：2019-04-07 16:52
【摘要】：我们在本文中要处理的半导体器件数学模型，它广泛地应用在太阳能电池、光电探测器、光电二极管、激光二极管等半导体器件的理论设计中.对于半导体器件设计而言，数值模拟是一种新兴的设计技术，对数值方法的研究在整个数值模拟过程中占有十分重要的位置.在实际生产中，人们希望较精确地得到电势ψ、电子浓度e、空穴浓度p的数值解，以指导半导体的理论设计.人们发现，电子位势不直接出现在浓度方程中，而它的梯度直接出现在浓度方程中.我们可以选择能够高精度逼近电势梯度的方法来提高浓度的逼近.考虑到浓度方程的对流占优性质，我们可以引入特征线法处理对流项.从而使数值模型能够更好地体现原始问题的物理本性. 本文旨在对下列的半导体器件数学模型建立能同时高精度逼近电势ψ、电场强度→u (→u=ψ)、电子浓度e、空穴浓度p的间断混合体积元方法和间断特征体积元方法.我们的论证表明，该方法继承了间断体积元的优点，即高精度、高并行性、空间构造简单、格式稳定.且能够通过电场强度→u的高精度计算更好地逼近浓度，，同时避免锋线前沿的数值弥散. 通过对提出的格式进行理论分析，我们得到了电势ψ的L2模、场强→u的H(div)模、电子浓度e的L2模和空穴浓度p的L2模最优阶的误差估计.
[Abstract]:In this paper, we deal with the mathematical model of semiconductor devices, which is widely used in the theoretical design of semiconductor devices such as solar cells, photodetectors, photodiodes, laser diodes, etc. As far as semiconductor device design is concerned, numerical simulation is a new design technology, and the research of numerical method plays an important role in the whole process of numerical simulation. In practical production, it is hoped that the numerical solutions of potential 蠄, electron concentration e and hole concentration p can be obtained more accurately in order to guide the theoretical design of semiconductors. It is found that the electron potential does not appear directly in the concentration equation, but its gradient appears directly in the concentration equation. We can choose the method which can approximate the potential gradient with high precision to improve the concentration approximation. Considering the convective dominant property of the concentration equation, we can introduce the characteristic method to deal with the convective term. So that the numerical model can better reflect the physical nature of the original problem. The aim of this paper is to establish the discontinuous mixed volume element method and the discontinuous characteristic volume element method for the following mathematical models of semiconductor devices, which can simultaneously approximate the electric potential 蠄, the electric field intensity (渭 = 蠄), the electron concentration e, the hole concentration p and the electric field intensity at the same time. Our demonstration shows that this method inherits the advantages of discontinuous volume element, that is, high precision, high parallelism, simple spatial structure and stable format. Moreover, the concentration can be approximated better by the high precision calculation of electric field intensity, and the numerical dispersion in front of front line can be avoided at the same time. Through the theoretical analysis of the proposed scheme, we obtain the error estimates of the optimal order of L2 mode of potential 蠄, H (div) mode of field strength, L2 mode of electron concentration e and L2 mode of hole concentration p.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.82
本文编号：2454243
[Abstract]:In this paper, we deal with the mathematical model of semiconductor devices, which is widely used in the theoretical design of semiconductor devices such as solar cells, photodetectors, photodiodes, laser diodes, etc. As far as semiconductor device design is concerned, numerical simulation is a new design technology, and the research of numerical method plays an important role in the whole process of numerical simulation. In practical production, it is hoped that the numerical solutions of potential 蠄, electron concentration e and hole concentration p can be obtained more accurately in order to guide the theoretical design of semiconductors. It is found that the electron potential does not appear directly in the concentration equation, but its gradient appears directly in the concentration equation. We can choose the method which can approximate the potential gradient with high precision to improve the concentration approximation. Considering the convective dominant property of the concentration equation, we can introduce the characteristic method to deal with the convective term. So that the numerical model can better reflect the physical nature of the original problem. The aim of this paper is to establish the discontinuous mixed volume element method and the discontinuous characteristic volume element method for the following mathematical models of semiconductor devices, which can simultaneously approximate the electric potential 蠄, the electric field intensity (渭 = 蠄), the electron concentration e, the hole concentration p and the electric field intensity at the same time. Our demonstration shows that this method inherits the advantages of discontinuous volume element, that is, high precision, high parallelism, simple spatial structure and stable format. Moreover, the concentration can be approximated better by the high precision calculation of electric field intensity, and the numerical dispersion in front of front line can be avoided at the same time. Through the theoretical analysis of the proposed scheme, we obtain the error estimates of the optimal order of L2 mode of potential 蠄, H (div) mode of field strength, L2 mode of electron concentration e and L2 mode of hole concentration p.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.82
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