Integration-based approach to evaluate the sub-threshold slope of MOSFETs

A unified look at the use of successive differentiation and integration in MOSFET model parameter extraction

“…In fact, a conceptually analogous but less well known successive operator ratio is the Integral-to-Current Ratio, or H 1 auxiliary function [16,19,22,23]. This H 1 function (its symbol is H because of historic reasons and should not be confused with a Hermite polynomial) was originally suggested as a means to extract the model parameters of p-n junction models at very low forward voltages [15].…”

“…Because numerical integration inherently diminishes measurement noise instead of enlarging it as differentiation does, our group has been advocating for a while the use of integration-based auxiliary functions, as an advantageous alternative to the traditionally used differentiation-based model parameter extraction techniques [15][16][17][18][19][20][21][22][23]. Numerical integration has already proved to be a useful tool for model parameter extraction in various situations where noisy experimental data is present [24], as well as for other kinds of analytical tasks, such as assessing harmonic distortion, for example [25][26][27].…”