We investigated the validity of the Natori formalism for realistic multi-layer quantum well FETs. We show that the assumption of a single layer (the channel) carrying all of the current density is far from reality in the sub-threshold region, where in fact most of the current density resides below the channel. Our analysis is based on comparing results of Natori calculations with experimental ones and on comparing with other first-principles calculations. If the Natori calculations are employed in the subthreshold region then a misleadingly small subthreshold slope would be obtained. We propose a way to remedy this inefficiency of this formulation so that it can be applicable to realistic many-layer devices. In particular we show that if the 1-dimensional quantum well of the Natori method enclosing the electron gas is expanded to include the supply layer-usually below the channel-and a proper ab initio potential is used to obtain its eigenvalues, then the Natori formula regains its validity. (C) 2017 Elsevier Ltd. All rights reserved.