A Compact Model Satisfying Gummel Symmetry in Higher Order Derivatives and Applicable to Asymmetric MOSFETs

Unification of MOS compact models with the unified regional modeling approach

“…His contribution in the "B-ref" model with "S/D by label" [30] (not by MOS convention), with velocity saturation occurring at the source or drain end depending on the terminal V d and V s , has made it possible for complete Gummel symmetry in any higher-order derivatives as well as physical modeling of asymmetric S/D devices. He also extended the URM for extrinsic charge and capacitance modeling in the S/D-gate overlap regions, with detailed one/two-iteration parameter extraction.…”

“…With the S/D identified by "label" (layout), velocity saturation may occur at the drain or source end depending on the terminal V d and V s , given by [30,33] …”

“…in which the saturation velocity v sat can be specified for different values at the S/D for modeling asymmetric S/D devices [30]. The transition function for the "G-ref" effective saturation voltage is given by [33] V c,eff = ϑ{V c , V c,sat , V cc ,sat ; δ} (c = s, d; c = d, s)…”

“…which becomes an extremely small value in subthreshold, and it requires highly accurate solutions for evaluation in the φ s -based I ds model (30). From the "pinned-φ s " approximation, φ s = 2φ F + V c , (44) becomes φ s ≈ V ds , and we replace V ds by the "G-ref" effective drain-source voltage, given by…”

“…The aforementioned I ds model is an exact odd function of V ds and satisfies the GST for any higher order [30,33]. Using (30) and following [11], the terminal-charge models are derived [8], in which the bulk-charge model adopts the unique URM based on (25) [19] …”