Transport effects and characteristic modes in the modeling and simulation of submicron devices

This paper has two major goals: (1) to study the effect of the common practice of neglecting the convective terms (inertial approximation) in the hydrodynamic model in the simulation of n+-n-n+ diodes and two dimensional MESFET devices; and, (2) to test analytical criteria, formulated in terms of characteristic values of the Jacobian matrix, as a method of determining the impact of first derivative perturbation terms in this model, and in related energy transport models. This characteristic value analysis can be thought of as generalizing the usual analytical solution of first order linear systems of ordinary differential equations with constant coefficients. Concerning (1), we find that the inertial approximation is invalid near the diode junctions, and near the contact regions of the MESFET device. In regard to (2), we find a proper arrangement of terms, expressing the flux, such that the first derivative part of the system is hyperbolic, both for the hydrodynamic model and the energy transport model. For the hydrodynamic model, two forms of the heat conduction term are studied, including the case of a convective term. This suggests and validates the use of shock capturing algorithms for the simulation. Acknowledgements: The first author is supported by the National Science Foundation under grant DMS-9123208. The second author is supported by the National Science Foundation under grant ECS-9214488 and the Army Research Office under grant DAAL03-91-G-0123 and DAAH04-94-G-0205. Computation supported by the Pittsburgh Supercomputer Center and by NAS. ∗Department of Mathematics, Northwestern University, Evanston, IL 60208 †Division of Applied Mathematics, Brown University, Providence, RI 02912