本篇論文主要開發一套半導體元件模擬程式，建立矩陣係數法是為了確保程式對於理論值的驗證。我們就能利用我們開發的模擬軟體，模擬各種維度的半導體元件。過去常遇到結果不收斂或是驗證值錯誤，藉由此方法，讀者可以更有效率找出程式中的問題。文中將會驗證矩陣中的係數，比較程式與手算的之間的誤差值，藉以驗證我們所建立的元件模擬的正確性。如此一來，不僅可以驗證程式架構的細節，爾後還能進行BJT等半導體元件模擬，來提升我們模擬電路的彈性度。

In this thesis, we develop a semiconductor element module system. This system can ensure the verification of the theoretical value of the formula by the matrix coefficient method. We can use the simulation system we developed to simulate semiconductor elements of various dimensions. In the past, the results were often not converged or the verification value was wrong. With this method, the reader can more efficiently find the problems in the device simulation by comparing the error values between the computer programs and the hand calculation. In this way, we can verify the details of the system, and can simulate semiconductor component such as BJT , in order to improve the flexibility of our semiconductor devices.

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