Accounting for the body effect in the compact modeling of an “extrinsic” MOSFET drain current in the linear and saturation regimes

We use a linear approximation for the threshold voltage dependence on the body bias to derive the equation for the equivalent output resistance of the “extrinsic” MOSFET in the saturation regime. Previously we derived an equation for the equivalent output resistance of the “extrinsic” MOSFET in the saturation regime, that is based on the “intrinsic” transistor finite output resistance in the saturation regime. But we did not account for the body effect, i.e., the threshold voltage dependence on the body bias applied between the source and the fourth (body) MOSFET terminal. For the earlier generations of MOSFETs, the theory predicts that threshold voltage is a sublinear function of the body bias. However, modern transistors with steep retrograde body doping profiles exhibit an approximately linear relationship between a threshold voltage and a body bias, which allowed us to include the body effect into the compact model of an “extrinsic MOSFET. In addition, we discuss the application of our results to the theory of a common-source amplifier with an NMOS transistor with source degeneration.