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 本篇論文討論矩陣係數驗證法，來幫助半導體元件模擬之程式開發。在過去經常面臨程式上不收斂或者結果錯誤，且常常束手無策，很困難解決，因此矩陣係數驗證法可以一步一步驗證出聯立方程式的係數值，並且保證確保能抓到錯誤。為了增加二維分析的彈性，我們採用重心法的三角形網格，在第一個三角形網格後面驗證係數值，檢查理論值與模擬值是否一致，以達驗證目的。最後，再將此三角形網格應用於其他半導體元件，如電阻、PN二極體、BJT等，並模擬其特性曲線。
 In this thesis, we discuss the matrix coefficient verification method to help develop programs for semiconductor device simulation. In the past, we often faced program non-convergence or had wrong results. We feel helpless and it is difficult to solve. Therefore, the matrix coefficient verification method can verify the coefficient values of simultaneous equations step by step, and ensure that errors can be caught. In order to increase the flexibility of the two-dimensional analysis, we use the triangle grid module to verify the coefficient values in the first triangle grid and check whether the theoretical value and the simulated value are consistent to achieve the verification. Finally, the triangular grid is applied to other semiconductor devices, such as resistors, PN diodes, BJT, etc., and simulate their characteristic curves.
 摘要 iAbstract ii誌謝 iii目錄 iv圖目錄 v表目錄 vii第一章 簡介 1第二章 二維電路模擬架構與偵錯 42.1電路模擬之基本架構 42.2 如何有效率偵錯程式 82.3 矩陣係數驗證之重要性 10第三章 二維三角形重心法的係數驗證 133.1三角形重心法之等效電路 133.2矩陣係數驗證 163.3電腦差分近似法求係數之探討 323.4電阻與PN二極體之模擬與驗證 34第四章 二維BJT半導體元件之應用 414.1二維BJT之結構分析 414.2 二維BJT網格模型之設計 434.3二維BJT與其特性曲線模擬 45第五章 結論 48參考資料 49
 [1] Y. M. Li, “Research on Development of Computer Simulation Methods for SemiconductorDevices and Nanostructures,” D. S. Thesis, Institute of Electronics, National Chiao TungUniversity, Taiwan, Republic of China, 2000.[2] R. A. Jabr, M. Hamad, Y. M. Mohanna, “Newton-Raphson Solution of Poisson’s Equationin a PN Diode,” Int. J. Electrical Eng. Educ., Jan. 2007.[3] M. S. Li, “Rectangular Transform of Trapezoidal Mesh and Its Application to CylindricalMOSFETs,” M. S. Thesis, Institute of EE, Nation Central University, Taiwan, Republic ofChina, 2011.[4] M. Bern, D. Eppstein, and J. Gilbert, “Provably good mesh generation,” J. Compute.System Sci., pp. 384–409, 1994[5] S. S. Kuo, “Computer applications of numerical methods” Additions-Wesley Pub.Co.1972.[6] D. M. Bressoud, “Appendix to A Radical Approcch to Real Analysis,” 2nd edition,2006[7] Robert L. Boylestad, Louis Nashelsky, “Electronic Devices and Circuit Theory,”Chapter2, Prentice Hall, 9 edition, 2005[8] H. J. Kai,“ Finding the internal vector fromthe plane equation in obtuse triangle elementfor 2D semiconductor device simulation,” M. S. Thesis, Institute of EE, National CentralUniversity, Taiwan, Republic of China, pp. 7-10, 2016.[9] W. T. Shen” Finding internal vector from the edge vector in obtuse triangle element for 2Dsemiconductor device simulation,” M. S. Thesis, Institute of EE, National CentralUniversity, Taiwan, Republic of China, pp. 5-8, 2016.[10] D. A. Neamen, Semiconductor Physics and Devices, 3rd ed. McGraw-Hill Companies Inc.,New York, 2003.
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