The equation for the saturation current of an intrinsic (without taking into account parasitic source and drain resistances) MOSFET can be found in textbooks. An extrinsic MOSFET has parasitic resistors in series with its source and drain terminals. The equation for the saturation current of an extrinsic MOSFET also can be found in textbooks. It accounts for the velocity saturation effect, but it does not account for the body effect and the effect of carrier mobility reduction due to the normal electric field under the gate. Modern transistors with steep retrograde body doping profiles exhibit a more or less linear relationship between a threshold voltage and a source-to-body bias. Previously we have incorporated the body effect into equation for the saturation current of an extrinsic MOSFET with steep retrograde body doping profile. Later we incorporated the effect of mobility reduction under the gate (without accounting for the body effect) into equation for the saturation current of an extrinsic MOSFET. Finally, we derived the equation for saturation current of an extrinsic MOSFET with steep retrograde body doping profile with accounting for the mobility reduction under the gate, velocity saturation and the body effect. The carrier mobility reduction is accounted for by the simplest approximation which is used in the MOSFET Level 3 compact model. The velocity saturation is accounted for by assuming the simplest linear-piecewise approximation for the drift velocity dependence on the electric field.
Turin et al. (Mon,) studied this question.