在這篇論文中，我們利用基本的線性零組件，來完成非線性元件的模擬，我們使用的基本線性包含零組件電壓源、電容以及電壓控制電流源。我們更進一步將元件內部參數，置於主程式中，便於使用者辨識及做調整。為了用線性零組件進行2-D元件的模擬，我們利用線性電壓控制電流源這個線性零組件，再利用牛頓-拉夫森法將運算得到的電流以及轉導，置入矩陣ADV = B，經由牛頓-拉夫森法可以求解到DV ，這個未知向量，利用此觀念，逐步取代二維模擬器(2D mixed-level simulator)中使用之非線性特殊零組件，在牛頓拉夫森建立公式ADV = B中，A矩陣含微分項，微分項可用解析解或數值解來得到，我們分別運用解析解及數值解完成二維元件模擬，並進行解析解與數值解結果驗證與時間比較。In this thesis, the basic linear components, which consist of voltage source, capacitor, and voltage-control current source, are employed to simulate the non-linear devices. The circuit parameters are explicitly defined at the main program for easier recognition and adjustment.To simulate 2-D semiconductor devices by linear elements, the nonlinear Poisson equation and the nonlinear carrier continuity equations are replaced by the linear voltage-controlled current source in the environment of the Newton-Raphson iteration. The matrix A in ADV = B include partial differentiation items which are obtained by both numerical differentiation and analytical differentiation in this thesis. The simulation results show a good accuracy between two methods.
