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/sup +/-n-n/sup +/ 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.>

Simulation results for the hydrodynamic model are presented for an n/sup +/-n-n/sup +/ diode by use of shock-capturing numerical algorithms applied to the transient model with subsequent passage to the steady state. The numerical method is first order in time, but of high spatial order in regions of smoothness. Implementation typically requires a few thousand time steps. These algorithms, termed essentially nonoscillatory, have been successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws of fluid mechanics. The presented semiconductor simulations reveal temporal and spatial velocity overshot, as well as overshoot relative to an electric field induced by the Poisson equation. Shocks are observed in the transient simulations for certain low-temperature parameter regimes.>

An introduction to the hydrodynamic model for semiconductor devices is presented. Special attention is paid to classifying the hydrodynamic PDEs (partial differential equations) and analyzing their nonlinear wave structure. Numerical simulations of the ballistic diode using the hydrodynamical device model are presented, as an illustrative elliptic problem. The importance of nonlinear block iterative methods is emphasized. Arguments for existence of solutions and convergence of numerical methods are given for the case of subsonic electron flow.>

Steady-state semiconductor-device simulation is studied. A mathematical analysis of the so-called Lipschitz constant of the Gummel map, in the Slotboom variables, is given in terms of the device diameter d and the band-bending. This constant is directly related to the convergence of Picard iteration, within a convex, compact solution set, determined by the steady state, Van Roosbroeck system maximum principles. Allowing for specified gradient singularities, of order cr /sup -1/2/, we obtain an asymptotic dependence of d /sup 5/2/ as d -> 0. Functions of sup-inf boundary values of the data also appear, particularly as related to doping concentrations, in the representation of the band-bending. For simplicity, constant mobilities and zero recombination are assumed, at thermodynamic equilibrium. The setting is general, but motivated by FET devices. For micron devices at room temperature, convergence and unique solutions are expected up to, perhaps, band-bending of 0.42 /sup -2/3/ log c(kT) electronvolts in width across the intrinsic energy level. The definition of the Gummel map used herein employs the potential equation as a fractional step, based upon given values of the Slotboom variables. The continuity equations are then solved for the values associated with the Gummel map. The condition given for convergence of Picard iteration also guarantees uniqueness of solutions of the device model for prescribed doping and contact conditions. Finally, the constant c is estimated on the basis of heuristic considerations.