半導體模型的間斷體積元方法
發(fā)布時間：2019-04-07 16:52
【摘要】：我們在本文中要處理的半導體器件數學模型，它廣泛地應用在太陽能電池、光電探測器、光電二極管、激光二極管等半導體器件的理論設計中.對于半導體器件設計而言，數值模擬是一種新興的設計技術，對數值方法的研究在整個數值模擬過程中占有十分重要的位置.在實際生產中，人們希望較精確地得到電勢ψ、電子濃度e、空穴濃度p的數值解，以指導半導體的理論設計.人們發(fā)現，電子位勢不直接出現在濃度方程中，而它的梯度直接出現在濃度方程中.我們可以選擇能夠高精度逼近電勢梯度的方法來提高濃度的逼近.考慮到濃度方程的對流占優(yōu)性質，我們可以引入特征線法處理對流項.從而使數值模型能夠更好地體現原始問題的物理本性. 本文旨在對下列的半導體器件數學模型建立能同時高精度逼近電勢ψ、電場強度→u (→u=ψ)、電子濃度e、空穴濃度p的間斷混合體積元方法和間斷特征體積元方法.我們的論證表明，該方法繼承了間斷體積元的優(yōu)點，即高精度、高并行性、空間構造簡單、格式穩(wěn)定.且能夠通過電場強度→u的高精度計算更好地逼近濃度，，同時避免鋒線前沿的數值彌散. 通過對提出的格式進行理論分析，我們得到了電勢ψ的L2模、場強→u的H(div)模、電子濃度e的L2模和空穴濃度p的L2模最優(yōu)階的誤差估計.
[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.
【學位授予單位】：山東師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O241.82
本文編號：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.
【學位授予單位】：山東師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O241.82
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