Two Carrier Semiconductor Device Models with Geometric Structure and Symmetry Properties

By: Gui-Qiang Chen, Joseph W. Jerome, Chi-Wang Shu, and Dehua Wang

We introduce a novel two carrier (electro) hydrodynamic model, which incorporates higher dimensional geometric effects into a one dimensional model. A rigorous mathematical analysis is carried out for the evolution system in the case of piezotropic flow, including realistic carrier coupling. The proofs are constructive in nature, making use of generalized Godunov schemes with a novel fractional step, steady-state component, and compensated compactness. Two important applications are studied. We simulate: (1) the GaAs device in the notched oscillator circuit; and, (2) a MESFET channel, and its steady-state symmetries. The first of these applications is the well known Gunn oscillator, and we are able to replicate Monte-Carlo simulations, based upon the Boltzmann equation. For the second application, we observe the effect of a symmetry breaking parameter, the potential bias on the drain.
This paper appeared in: Modelling and Computation for Applications in Mathematics, Science, and Engineering, Oxford University Press (J. Jerome, ed.), 1998, pp. 103--140, and can be viewed in the following format: