超短沟道MOSFET电势的二维半解析模型

A 2D semi-analytical model for the potential distribution of ultra-short channel MOSFET

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.

Based on the principle of ultra-short channel MOSFET, a definite solution of potential is proposed by introducing two rectangular sources between the insulated gate and the space-charge region. By using the semi-analytical method and the spectral method, the 2D semi-analytical solution has been obtained for the first time as faras we know. The solution is a special function for the infinite series expressions. The most advantage of this model is that it can not only be calculated directly without numerical analysis but also keep the same accuracy as that of numerical solution. In addition, this model, which can be directly used in circuit simulation, has the characteristics that in its expression there is no adapter parameter with small calculating amount. The potential, surface potential and threshold of 45—22 nm MOSFET have been calculated in the frame of this model. It is shown that the calculated results are identical with Medici.