A CAD-compatible closed form approximation for the inversion charge areal density in double-gate MOSFETs

In developing the drain current model of a symmetrically driven, undoped (or lightly doped) symmetric double-gate MOSFET (SDGFET), one encounters a transcendental equation relating the value of an intermediate variable β (which is related to the inversion charge areal density and also surface-potential) to the gate and drain voltages; as a result, it doesn’t have a closed form solution. From a compact modeling perspective, it is desirable to have closed form expressions in order to implement them in a circuit simulator. In this paper, we present an accurate closed form approximation for the inversion charge areal density, based on the Lambert-W function. We benchmark our approximation against other existing approximations and show that our approximation is computationally the most efficient and numerically the most robust, at a reduced but acceptable accuracy. Hence, it is suitable for use in implementing inversion charge based compact models.