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.

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