1/4球面網格的構建及半導體元件的模擬

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：78

、訪客IP：3.145.2.95

姓名

林品辰(Pin-Chen Lin) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

1/4球面網格的構建及半導體元件的模擬
(Construction of 1/4 Spherical Grid and Simulation of Semiconductor Devices)

相關論文

★ 表面電漿共振效應於光奈米元件之數值研究	★ 金氧半電容元件的暫態模擬之數值量測
★ 雙載子電晶體在一維和二維空間上模擬的比較	★ 改善後的階層化不完全LU法及其在二維半導體元件模擬上的應用
★ 一維雙載子接面電晶體數值模擬之驗證及其在元件與電路混階模擬之應用	★ 階層化不完全LU法及其在準靜態金氧半場效電晶體電容模擬上的應用
★ 探討分離式簡化電路模型在半導體元件模擬上的效益	★ 撞擊游離的等效電路模型與其在半導體元件模擬上之應用
★ 二維半導體元件模擬的電流和電場分析	★ 三維半導體元件模擬器之開發及SOI MOSFET特性分析
★ 元件分割法及其在二維互補式金氧半導體元件之模擬	★ 含改良型L-ILU解法器及PDM電路表述之二維及三維元件數值模擬器之開發
★ 含費米積分之高效率載子解析模型及其在元件模擬上的應用	★ 量子力學等效電路模型之建立及其對元件模擬之探討
★ 適用於二維及三維半導體元件模擬的可調變式元件切割法	★ 整合式的混階模擬器之開發及其在振盪電路上的應用

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

本論文的主旨為利用 C 語言去模擬 1/4 球面網格之半導體元件，一開始利用
有限元素法去建立最基本的網格，進而將網格構成的單位元素等效成等效電路模
型以便將方程式(如帕松方程式和電子電洞連續方程式)帶入電路模型中進行運
算求所需之物理和電路特性。在架構建立完之後，可以透過網路上的動態幾何代
數軟體(GeoGebra)去塑造所期望的 1/4 球面網格，先在球座標上架構所需的點數
到運用體積比驗證我們的 1/4 球面網格建構是否精準，最後模擬我們想要的元件
特性曲線，可得知結果與理論值相差無幾，說明了我們此套開發的程式模擬架構
是能應用在 1/4 球面網格半導體元件的模擬。

摘要(英)

The main purpose of this thesis is to use C language to simulate the semiconductor
element of the 1/4 spherical grid. In the beginning, the finite element method is used to
establish the most basic grid, and then the unit element grid can transform into an
equivalent circuit, which can convert the Equations (such as the Poisson equation and
the electron-hole continuity equation) to obtain the required physical and circuit
characteristics. After the architecture is established, we can use the dynamic geometric
algebra software (GeoGebra) to shape the 1/4 spherical grid. First, we set the nodes in
spherical coordinates and then used the volume ratio to verify the accuracy of the
1/4 spherical grid structure. Finally, we can simulate the characteristic curve we want
to show that the simulation results are almost the same as the theoretical values, which
shows that the program simulation framework we developed can be applied to the
simulation of 1/4 spherical grid semiconductor devices.

關鍵字(中)

★ 半導體元件模擬
★ 球面網格的構建
★ 1/4球面網格
★ 1/4球殼網格

關鍵字(英)

★ Simulation of Semiconductor Devices
★ Construction of Spherical Grid
★ 1/4 Spherical Grid
★ 1/4 Spherical Shell Grid

論文目次

目錄
頁次
摘要......................................................................................... i
Abstract ................................................................................... ii
誌謝.........................................................................................iii
目錄..........................................................................................iv
圖目錄.........................................................................................v
表目錄..................................................................................... viii
第一章簡介................................................................................... 1
第二章三維半導體元件模擬之架構及應用........................................................... 3
2.1 三維半導體元件網格模型建構 ................................................................ 3
2.2 三維半導體元件網格模型運算 ................................................................ 5
2.3 三維半導體等效電路模型之方程式應用 ........................................................ 10
2.4 三維六面體之基本電阻模擬分析 ............................................................. 20
2.5 三維六面體之 PN Junction 模擬分析 .........................................................22
2.6 三維六面體之 MOS Capacitor 模擬分析 ...................................................... 25
第三章 1/4 球體半導體元件模擬之架構及應用....................................................... 27
3.1 1/4 球體網格的構建 ....................................................................... 27
3.2 1/4 球體網格的體積比 ......................................................................30
3.3 1/4 球體網格的模擬應用 ................................................................... 33
第四章 1/4 球殼半導體元件模擬之架構及應用....................................................... 35
4.1 1/4 球殼網格的構建 ....................................................................... 35
4.2 1/4 球殼網格的體積比 ..................................................................... 41
4.3 1/4 球殼網格的模擬應用 ................................................................... 43
第五章結論.................................................................................. 46
參考文獻..................................................................................... 47

參考文獻

[1] L Baker, “C Mathematical Function Handbook”, Computing McGraw-Hill,
Oct.1991.
[2] T. D. Pauw and W. F. Pfeffer, “The Divergence Theorem for Unbounded Vector Fields”, Transactions of the American Mathematical Society, Vol. 359, No. 12, pp. 5915 - 5929, American Mathematical Society, Dec. 2007.
[3] R.A.Jabr, M. Hamad and Y.M. Mohanna, “Newton-Raphson Solution of Poisson’s Equation in a PN Diode”, International Journal of Electrical Engineering Education, Jan. 2007.
[4] N. Mohamed and M. Z. Sujod, “Finite Elements in Semiconductor Devices ”, 2009 International Conference on Information Management and Engineering, pp.108-110, Apr. 2009.
[5] Y.T.Liao, “3D Bridged Cube Element and Matrix Coefficient Verification and Its Applications to Semiconductor Device Simulation” National Central University, M.S.Thesis, June.2021.
[6] R.E.Bank, D.J.Rose, and W.Fichtner, “Numerical methods for semiconductor device”, IEEE Trans, Electron Devices, Sep.1983.
[7] Y.P.Chen, “3D grounded Cube Element and Matrix Coefficient Verification and Its Applications to Semiconductor Device Simulation” National Central University, M.S.Thesis, June.2021.
[8] J.F.Lee, “2D grounded Triangle Element and Matrix Coefficient Verification and Its Applications to Semiconductor Device Simulation” National Central University, M.S.Thesis, June. 2021.
[9] S. Micheletti, “Stabilized finite elements for semiconductor device simulation,” Compute & Visual Sci., vol. 3, pp. 177-183, 2001.
[10] D.A.Neamen, “Semiconductor physics and devices” 4th edition. McGraw-Hill, Jan.2011.
[11] M. Marrero-Martín, J. García, B. González and A. Hernández, "Circuit models for PN integrated varactors," IEEE Trans, Palma de Mallorca, pp. 1-4, 2011.
[12] M. Putti and C. Cordes, “Finite Element Approximation of the Diffusion Operator on Tetrahedra”, SIAM J. SCI. COMPUT., Vol. 19, No. 4, pp. 1154 – 1168, Society for Industrial and Applied Mathematics, July 1998.
[13] P. Feldmann and R.A. Rohrer, “Proof of the Number of independent Kirchhoff Equations in an Electrical Circuit”, IEEE Transactions on Circuits and Systems, vol. 38, No. 7, pp.681 - 684, IEEE, Jul. 1991.

指導教授

蔡曜聰(Yao-Tsung Tsai)

審核日期

2022-7-6

推文