CLAWPACK Simulation of the Classical Hydrodynamic Model for
Semiconductor Devices (Master's defense)
Abstract
The classical hydrodynamic model has become a standard simulation tool
with the capability of describing important "hot electron" phenomena
in submicron semiconductor devices. As a result, the need to compute
accurate solutions is crucial. The classical hydrodynamic model is
composed of nonlinear conservation laws for particle number, momentum,
and energy, coupled with Poisson's equation for the electric
potential. Thus the hydrodynamic model PDEs possess elliptic,
hyperbolic, and parabolic modes. The nonlinear hyperbolic modes
support shock wave solutions.
To accurately compute solutions including high resolution of shock
waves, the classical hydrodynamic model equations were implemented in
LeVeque's software package CLAWPACK (Conservation LAWs PACKage).
CLAWPACK consists of routines for solving time-dependent hyperbolic
systems of conservation laws based on higher-order Godunov methods.
Steady-state simulations of the classical hydrodynamic model
(including shock waves) will be presented using CLAWPACK of the
n+/n/n+ diode, which models the channel of a field effect transistor.
A splitting method is used to incorporate the source terms in the
hydrodynamic equations. Appropriate numerical methods for solving the
differential equation which arises in this method are discussed. The
need for an L-stable method to avoid spurious local oscillations
("ringing") will be emphasized.
