本篇論文的主要目是討論二維三角形網格的開發與矩陣係數驗證的重要性，以矩陣係數法為基礎驗證我們所架構的電路模型，並以我們設計的程式去模擬各種類的半導體元件特性。透過對矩陣係數的驗證來確保程式運算時的準確性，再以兩種不同的運算方法來探討同一個運算模型，分別為接地式與非接地式矩陣係數驗證，藉由此方法能夠提高程式運算的精準度。而我們論文中皆採取重心法來驗證三角形網格模型，而此方法好處在於能夠對任意三角形進行驗證，保證程式可符合任意情況。最後，我們以此為出發點模擬出電阻、PN二極體、BJT或其餘特殊半導體元件等模型的電路特性，模擬其特性曲線並與物理意義相互對照，以確保程式的真偽性。

The main purpose of this thesis is to discuss the importance of the development of 2D triangle element and matrix coefficient verification. Based on the matrix coefficient method, we will verify the circuit model that we have constructed,and use our designed program to simulate various types of semiconductor devices characteristics. Through the verification of the matrix coefficients to ensure the accuracy of the formula calculation, two different calculation methods are used to explore the same calculation model, namely the grounded and the bridged matrix coefficient verification. In our thesis, the center of gravity method is used to verify the triangle mesh model. The advantage of this method is that it can verify any triangle and ensure that the program can satisfy any situation. Finally, we use this triangle model as a starting point to simulate the circuit characteristics of devices such as resistors, PN diodes, BJTs or other special semiconductor devices, simulate their characteristic curves and compare them with physical significance to ensure the authenticity of our program.

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