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

Abstract

This paper presents a new nonquasi-static (NQS) model for the MOSFET. The model is derived from physics and only relies on the very basic approximation needed for a charge-based model. To derive the model, a popular variational technique named Galerkin's Method has been used. The model proves to be very accurate even for extremely fast changes in the bias voltages. Simulation results show a very good match even when the rise time of the applied signal is smaller than the transit time of the device.

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

“…We want to investigate how the channel reaches its new steady state, i.e., how changes with time. In this special case, for , (16) in [1] reduces to 1There is no term, because under our assumption, for . Now, under the small-signal assumption, since the change in the voltage is small, will also be small.…”

“…The small-signal model presented here is essentially an extension of the large-signal model described in [1]. We begin with the assumption that the n-MOSFET channel is in steady state.…”

“…In order to determine the 's, we need to find the initial condition. From the definition of [1], we have…”

“…denotes the contribution of th harmonic to the terminal . For example, with our choice of basis functions as [1] for the drain terminal, . If is very small (i.e., it does not disturb the bias condition which is true under small signal assumption), we can think of the system as a linear one and use superposition theorem to calculate the various NQS charges.…”

“…(23) and can be determined from boundary condition [see (24), (25), shown at the bottom of the page] consists of both QS and NQS parts Using (21), it can be shown that (26) After finding, we can easily obtain the small-signal NQS current. Using the relations given in Section III of[1], in s domain, we have…”