Discretization of Semiconductor Device Problems (II)

Enhanced functional integration in modern electron devices and the ensuing device miniaturization requires an accurate modeling of transient energy transport in semiconductors in order to describe high-field phenomena such as hot electrons, impact ionization and high frequency oscillations. For these reasons macroscopic models like the drift-diffusion equations (and the augmented ones) are no longer adequate and it has became almost mandatory to resort to a set of moment equations obtained from the semiconductor Boltzmann transport equation, which form a system of hyperbolic equations. From a computational point of view this has prompted the use of suitable numerical schemes which are able to cope with the dominantly hyperbolic nature of the problem, the coupling with the Poisson equation and the stiffness of the source term.