Convergent Iterative Schemes for a Non-isentropic Hydrodynamic Model for Semiconductors

Abstract

Two iterative schemes for the solution of the one-dimensional stationary full hydrodynamic model for semiconductor devices are studied. This model consists of a system of balance equations for the electron density, temperature, and the electric field. The first iterative scheme relies on a decoupling of the equations in the spirit of the well-known Gummeliteration for the standard drift diffusion model. Convergence is proven in the case of small deviations from the equilibrium state. Secondly, a full Newton-iteration is analyzed and its local second order convergence is proven.