On the hydrodynamic model for semiconductor devices

Li-Ming Yeh, Purdue University

Abstract

The object of this research is to further understand the hydrodynamic model for semiconductor devices derived from moments of the Boltzmann's equation. The existence of the Euler-Poisson model, a simplified version of the hydrodynamic model, for unipolar semiconductor devices at steady state is examined first. The nonlinear partial differential equations of the model consist of the steady state Euler equations of gas dynamics with the addition of a velocity relaxation term, coupled to Poisson's equation for the electric potential. First, by prescribing the vorticity on the inflow boundary, the small normal component of velocity on the whole boundary, and assuming a small variation of the velocity relaxation time in the entire semiconductor domain, the existence of a smooth subsonic solution is demonstrated. Then, ways of prescribing possible vorticities on the inflow boundary so that subsonic solutions exist are discussed. The hydrodynamic model is then applied to a transient case. The well-posedness of the problem described by the model is investigated. Under appropriate subsonic boundary conditions, the existence of a unique local-in-time subsonic solution is demonstrated. Appropriate boundary conditions for different boundary value problems associated with this model are also discussed. A numerical method for the hydrodynamic model in the one-dimensional case is also studied. A second order accurate-in-time scheme is presented for the subsonic solution of this model. The stability and the convergence of this scheme are established, and optimal order error estimate is demonstrated.

Degree

Ph.D.

Advisors

Douglas, Purdue University.

Subject Area

Mathematics

COinS