TY - JOUR

T1 - Transport Effects and Characteristic Modes in the Modeling and Simulation of Submicron Devices

AU - Jerome, Joseph W.

AU - Shu, Chi Wang

N1 - Funding Information:
The comput&ion was supported by the Pittsburgh Supercomputer Center and by NAS.
Funding Information:
where the right-hand-side .(W) contains both the forcing terms due to the relaxation, which are nonlinear functions of w, and the second derivative terms due to the heat conduction. A necessary precondition for the usage of hyperbolic based shock capturing algorithms is the property that the first derivative part, fl(w), + f2('~)~, is indeed hyperbolic, i.e., &f;(w)+ Manuscript received Apnl 13,1994;r evised February 9, 1995. The work of J. W. Jerome is supported by the National Science Foundation under Grant DMS-9123208.T he work of C.-W. Shu is supported by the National Science Foundation under Grant ECS-9214488a nd the A m y Research Office under Grants DAALO3-914-0123 and DAAH04-94-G-0205.Th is paper was recommended by Associate Editor J. White.

PY - 1995/8

Y1 - 1995/8

N2 - 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.

AB - 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.

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U2 - 10.1109/43.402490

DO - 10.1109/43.402490

M3 - Article

AN - SCOPUS:0029357294

VL - 14

SP - 917

EP - 923

JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

SN - 0278-0070

IS - 8

ER -