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

• Unified view of successive differential and integral operator use in MOSFET model parameter extraction.
• Comparative assessment of representative extraction procedures.
• A new minimalist MOSFET transfer characteristics model is used for comparison.
• The abridged model is based on a single polylogarithm function of gate voltage.
• Comparative examples of parameter extraction from measured current of real nanometric MOSFETs.

This article provides a unified look at MOSFET model parameter extraction methods that rely on the application of successive differential and integral operators, their ratios, and various other combinations thereof. Some of the most representative extraction procedures are assessed by comparatively examining their ability to extract basic model parameters from synthetic MOSFET transfer characteristics, generated by an ad hoc minimalist four-parameter model. The model used, comprised of a single polylogarithm function of gate voltage, approximately describes in a very concise manner the essential features of MOSFET drain current continuously from depletion to strong inversion. The exponential-like low voltage and monomial-like high voltage asymptotes of this simple model are conveniently used to analyze and compare the different extraction schemes that are founded on successive differentiation or integration. In addition to providing a combined view useful for comparative methodological appraisal, the present unified analysis facilitates visualizing and exploring other potentially promising extraction strategies beyond the straightforward use of successive differential and integral operators and their ratios. We include examples of parameter extraction from measured transfer characteristics of real experimental MOSFETs to comparatively illustrate the actual numerical implementation of typical successive differential and integral operator-based procedures.