A Physics-Based, SPICE (Simulation Program with Integrated Circuit Emphasis)-Compatible Non-Quasi-Static MOS (Metal-Oxide-Semiconductor) Transient Model Based on the Collocation Method

Abstract

The collocation method has been applied to derive a new SPICE (Simulation Program with Integrated Circuit Emphasis)-compatible non-quasi-static MOS (metal-oxide-semiconductor) transient model. Contrasting to the conventional approximation methods, the collocation method is simple for the model derivation and efficient in optimizing the variables of the continuity equation. The derived model is fully physics-based in that all the transient currents are directly expressed by only physically meaningful, optimized quantities. The model adequately predicts transient currents in the bias region such as the weak inversion region where conventional models show numerical difficulties.

A new approach to model nonquasi-static (NQS) effects for mosfets-part I: large-signal analysis

“…The MOSFET inversion layer charge can be expressed in simple form in terms of the surface potential using the charge sheet approximation. Assuming an n-channel device, the inversion charge per unit area is given as a function of position along the channel (positive direction is from source to drain ) and time by (6) where is the surface potential and is the body factor. The current is given by (7) where the first term represents the diffusion component and the second term represents the drift component.…”

“…But this model assumes a very simple quadratic charge profile. Hwang et al [6] improved this work by using collocation method instead of weighted residue method, but their work also assumes the same charge profile. Park, Ko, and Hu [7] developed a NQS model with a general charge profile.…”

Parameter extraction for relaxation-time based non-quasi-static MOSFET models

“…NQS behavior can be modeled accurately using multi-segment models [1], [2] or the spline collocation technique [3], [4]. Both of these approaches have the significant and convenient practical attribute that they are based purely on physical analysis and have no extractable parameters; to use them you merely turn them on, you do not have to make detailed and often difficult high frequency or fast transient measurements and then fit the models to the measured data.…”