在積體電路的設計和發展上，半導體的數值模擬分析扮演一個非常重要的角色。一些在實驗上或解析模型上觀察不到的元件電性，就可藉由元件的模擬來觀察。但是在半導體元件的數值模擬過程中，往往需要解非常龐大的稀疏矩陣，所以在本論文中，將就半導體元件的模擬特性來改善階層化不完全LU分解法 (Levelized Incomplete LU method)，並用來開發一個新的稀疏矩陣解法器。而在元件和半導體的混階模擬上，我們將描述載子傳輸的擴散模型藉由專業的技術加以分離，以轉換成一些等效電路元件，例如電壓控電流源、電容和電壓控制電壓源等。因此就可使用一般的電路模擬器來做混階模擬。 最後，我們將使用二極體開關電路和金氧半場效電晶體，配合新的電路模擬器進行一維和二維混階模擬，並對元件的特性進行分析和討論。在模擬過程中，我們也會比較改善後的矩陣解法和傳統解法在模擬速度上的差異。 Numerical simulation of semiconductor device plays a very important role in the design and development of integrated circuits. In this thesis, we will present a new circuit simulator with improved Levelized Incomplete LU method to perform the simulation. To have an environment for evaluating the interaction between semiconductor device and the circuit, we use the equivalent circuit approach. This approach allows for the simple representation carrier transport models of devices through equivalent circuit elements such as voltage controlled current sources and capacitors. Therefore, we can perform the mixed-level simulation in general circuit simulators. We will take PN diode switching circuit and MOSFET as examples to test our equivalent circuit model and the improved circuit simulator. The comparison between improved matrix solution method and the conventional method will be demonstrated in this thesis too.
