2DEG-3DEG charge transport model for MOSFET based on the maximum entropy principle (Q2862273)

The authors study the effects of quantum confinement in a MOSFET, which causes the presence of 2-D electrons in the channel under the gate, where they coexist with 3-D electrons. The confinement is in the direction transversal to the oxide and is modelled by a 1-D Schrödinger equation which gives rise to subbands. In the longitudinal directions, for channels longer than 40 nanometers, the 2-D electron transport can be described, with good approximation, semiclassically. Starting from the respective Boltzmann transport equations and using the moment method, a hydrodynamical model is constructed for 2-D and 3-D electrons, which takes into account all the main scattering mechanisms of those electrons with phonons. Also transitions from 2-D to 3-D electrons and vice versa are considered, which are respectively due to the absorption and the emission of a nonpolar optical phonon. The closure relations are obtained by means of the maximum entropy principle, and, in particular, a suitable expression for the 2-D electron entropy is introduced. Eventually, by a diffusion scaling, the authors also deduce an energy transport model whose parabolicity is proved.