Showing papers by "Vittorio Romano published in 2006"

Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors

Abstract: Nonlinear asymptotic Lyapunov stability of the equilibrium state for the balance equations of charge transport in semiconductors based on the maximum entropy principle [A.M. Anile, V. Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Contin. Mech. Thermodyn. 11 (1999) 307–325; V. Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin. Mech. Thermodyn. 12 (2000) 31–51] is proven for a typical 1-D problem.

Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors

Abstract: Linear asymptotic Lyapunov stability of the equilibrium state for the balance equations of charge transport in semiconductors based on the maximum entropy principle [AM Anile, V Romano, Non parabolic band transport in semiconductors: closure of the moment equations, Contin Mech Thermodyn 11 (1999) 307–325; V Romano, Non parabolic band transport in semiconductors: closure of the production terms in the moment equations, Contin Mech Thermodyn 12 (2000) 31–51] is proven for a typical two-dimensional problem

Symmetry Analysis for the Quantum Drift-Diffusion Model of Semiconductors

Abstract: semiconductors, based on the Bohm potential, is performed and example of exact solutions are given. 1. The model In the last years continuum models for the description of charge carrier transport in semiconductors have interested applied mathematicians and engineers on account of their applications in the design of electron devices. Simple macroscopic models widely used in engineering applications are the

Exact Closure Relations for the Maximum Entropy Moment System in Semiconductor Using Kane’s Dispersion Relation

Abstract: The maximum entropy moment systems of the Boltzmann equation is only solvable with physically unrealistic restrictions on the choice of the macroscopic variables. We show that no such difficulties appear in the semiconductor case if Kane’s dispersion relation is used for the energy band of electrons. As an application the 5-moment model is discussed.

Gunn Oscillations Described by the MEP Hydrodynamical Model of Semiconductors

Abstract: High-field phenomena in submicron electron devices cannot be described satisfactorily within the framework of the drift-diffusion models that do not include energy as a dynamical variable and are valid only in the quasi-stationary limit, while most hydrodynamical models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem [1]. Here we employ a moment approach, previously introduced in [2, 3] (see also [4] for a complete review) in which the closure procedure is based on the maximum entropy principle while the conduction bands are described by the Kane dispersion relation. The electrons in GaAs are considered as a mixture of two fluids, one representing the electrons in the Γ -valley and the other the electrons in the four equivalent L-valleys. The model comprises the balance equations of electron density, energy density, velocity and energy flux for both populations, coupled to the Poisson equation for the electric potential. We will give only a brief sketch of the model. For more details the interested reader is referred to [5]. One assumes that the conduction band is described in the neighborhood of each minimum (valley) by the Kane dispersion relation approximation