Abstract
A nonlinear wave approach is suggested for analyzing systems of balance equations used for modeling nonstationary and hot-carrier dynamics in semiconductors. The approach is applicable since balance equations in conventional use comprise quasilinear systems of partial differential equations, and so are describable naturally in terms of nonlinear hyperbolic waves. A general review of the pertinent wave properties is given for systems written in one space dimension and time for an arbitrary number of conserved quantities. Special attention is paid to the peculiar roles of flux, source, and relaxation terms in specifying signal speeds and wave types, and in controlling wave interaction. The pervasive nature of discontinuous solutions, and the possibility of nonlinear resonance phenomena are discussed. The latter are claimed to have important consequences for the numerical resolution and stability of solutions, and for device behavior. Certain restrictions on the proper posing of initial-boundary value problems are stressed. These ideas are illustrated in particular for the single-electron gas version of the semi-empirical transport equation model for GaAs. This model uses fluxes and relaxation rates taken from steady-state Monte Carlo data to describe the spatial and temporal evolution of the three conserved quantities: particle density, velocity field, and energy. Geometrical effects resulting from variation of the channel cross section have been introduced into the discussion.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call