本論文著重在以二維等效電路模型利用階層化不完全LU分解法進行準靜態金氧半場效電晶體電容的模擬分析。在二維的元件模擬中，傳統的LU分解法產生大量的非零項，消耗大量的記憶體空間，二維的元件模擬往往無法在個人電腦上進行，階層化不完全LU分解法解決此一問題。在模擬的過程中，採用金屬閘極的結構和交錯式的變數排列方法，這是因為金屬閘極的結構較多晶矽閘極結構節省許多格子點，交錯式的變數排列方式更有效降低非零項的產生。本論文使用電荷法(charge method)， 弦波法(sinusoidal method)， 斜波法(ramp method)三種方法模擬量測準靜態金氧半場效電晶體閘極-基極電容、閘極-源極電容、閘極-吸極電容，並分析比較模擬結果。最後，我們也嘗試改變資料儲存的型態以節省記憶體空間，然而效果非常有限，因而建議一種個別求解的方式(decoupled method)以減少非零項的產生，有效利用記憶體空間。

In this thesis, we focus our attention on the measurement of the quasi-static MOSFET capacitance and Levelized incomplete LU method. Direct LU decomposition is not suitable for large-scale device simulation, because a lot of fill-ins will be generated during LU decomposition. Levelized incomplete LU method provides a good way to improve traditional LU decomposition. The structure of the metal gate and the method of the interleaving variable permutation are used. The use of the metal gate can save some rectangular grids which are used to describe the poly gate terminal. The use of the interleaving method reduces the number of fill-ins. In the meantime, the main focus of this thesis is on the measurement of gate to substrate, gate to source, and gate to drain capacitances of MOSFET. These measurements are implemented by charge method, sinusoidal method, and ramp method. The results of C-V characteristics are compared. Finally, we try to reduce memory space by changing the data type, but it is quite difficult. Therefore, we proposed decoupled method to reduce the number of nonzero entries.

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