A quasi‐variational inequality for the simulation of a MODFET transistor

We introduce the drift‐diffusion model with appropriate jump conditions at the junction of the MODFET transistor (AlGaAs/GaAs). We propose a quasi‐variational inequality (QVI) model for this device. We assume that the electron density is bounded and piecewise constant. These hypotheses imply that the Poisson’s equation becomes linear with respect to the electrostatic potential. The QVI model keeps a coupling with the continuity equation. Free boundaries arise in the medium AlGaAs near the Schottky‐gate contact and in the high mobility medium (GaAs) under the effect of the electron affinity discontinuity at the junction. Numerical results of the QVI model show their location versus the applied gate voltage V/up> and the molar fraction X of the Al_XGa_(1‐X)As medium. The inequality seems to be a reasonable simplification of the non‐linear Poisson’s equation.