本論文主要為開發一套有效率的載子濃度計算之解析解模型，此解析解模型是以費米積分為基礎，並將其延伸到三段及五段式解析模型載子濃度計算方法。使用此模型將不再需要任何的數值積分方法，並且此解析解模型比傳統的費米數值積分方法還要快三十九倍。為了印證所開發之載子濃度計算方法的正確性，我們也使用Medici操作手冊提供的載子濃度計算模型來印證並且與其他的解析模型比較之。而我們也將此模型加以改良使得我們的金氧半導體之源極、汲極與基板能摻雜到更高等級的濃度。並且，我們也利用我們已開發的模型來探討在金氧半導體電容與金氧半導體元件的半導體電荷及其在放大器元件上的應用。 In this thesis, we develop an efficient analytical model for carrier calculation. This model is based on the Fermi-Dirac integral, and extends it from the Three-Region to Five-Region analytical model of carrier calculation. No numerical integral is needed in the new model. And the running time of Fermi-Dirac numerical integral is thirty-nine times slower than our analytical models. For verifying the correctness of the analytical model of carrier calculation, we use a carrier calculation model including the Fermi-Dirac carrier statistics in Medici and an analytical model of Shur. Moreover, we apply our model to the MOSFET that allows high doping in the source, drain and substrate regions. Furthermore, we use the developed model to discuss the semiconductor charge of MOS-C and the amplifier application of MOSFET.
