Smoothing globally continuous piecewise functions based on limiting functions for device compact modeling

摘要

This paper generalizes a smoothing method for globally continuous piecewise functions based on limiting functions, with and without considering symmetry. The resulting function is infinitely differentiable. The method uses an upper limiting function, a lower limiting function, and a both-side limiting function. Three forms of the upper limiting functions are reviewed, namely square root, power, and log-exp. A general method of constructing the lower and both-side limiting functions from the upper limiting function is developed. All missing limiting functions in the three forms are derived, and the set is complete. The monotonicity of the limiting functions is proved. The usage in device compact modeling is demonstrated. In general, this method is better than the window-function-based method.