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本文根据超短沟道MOSFET的工作原理,在绝缘栅和空间电荷区引入两个矩形源,提出了亚阈值下电势二维分布的定解问题.通过半解析法和谱方法相结合,首次得到了该定解问题的二维半解析解,解的结果是一个特殊函数,为无穷级数表达式.该模型的优点是避免了数值分析时的方程离散化,表达式不含适配参数、运算量小、精度与数值解的精度相同,可直接用于电路模拟程序.文中计算了沟道长度是45—22nm的MOSFET电势、表面势和阈值电压.结果表明,新模型与Medici数值分析结果相同.
According to the working principle of ultra-short channel MOSFET, two rectangular sources are introduced into the insulated gate and the space charge region, and a two-dimensional distribution problem of sub-threshold potential is proposed.Through the combination of semi-analytical method and spectral method, The result of the solution is a special function, which is an infinite series of expressions.The advantage of this model is that it avoids the discretization of equations in numerical analysis, the expression does not contain the fitting parameters, The computational complexity is small and the precision is the same as that of the numerical solution.It can be directly used in the circuit simulation program.The MOSFET potential, surface potential and threshold voltage with the channel length of 45-22nm are calculated.The results show that the new model and the Medici numerical analysis the same.