Finite-element Discretizations of Semiconductor Energy-transport Equations

Energy-transport models describe the flow of electrons in a semiconductor crystal. Several formulations of these models, in the primal or dual entropy variables or in the drift-diffusion-type variables, are reviewed. A numerical discretization of the steady-state drift-diffusion-type formulation using mixed-hybrid finite elements introduced by Marini and Pietra is presented. The scheme is first applied to the simulation of a one-dimensional ballistic diode with non-parabolic band diagrams. Then a two-dimensional deep submicron MOSFET device with parabolic bands is simulated, using an adaptively refined mesh.