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

Linear 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 two-dimensional problem.     

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

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.     

Electron-phonon hydrodynamical model for semiconductors

A hydrodynamical model for the electron-phonon system in semiconductor is developed by closing the moment system arising from the coupled Boltzmann equations for electrons and phonons with the maximum entropy principle. Limiting models are obtained under appropriate scaling, and comparisons with the existing models of charge transport in semiconductors including the thermal effects of the crystal lattice are presented.     

Electron-phonon hydrodynamical model for semiconductors

A hydrodynamical model for the electron-phonon system in semiconductor is developed by closing the moment system arising from the coupled Boltzmann equations for electrons and phonons with the maximum entropy principle. Limiting models are obtained under appropriate scaling, and comparisons with the existing models of charge transport in semiconductors including the thermal effects of the crystal lattice are presented.     

Justification of the stabilization method for a mathematical model of charge transport in semiconductors

An initial boundary value problem for a quasilinear system of equations is studied and effectively applied to numerically determine, by the stabilization method, stationary solutions of a hydrodynamic model describing the motion of electrons in the silicon transistor MESFET (metal semiconductor field effect transistor).     

Stability of stationary states of a quantum energy transport model for semiconductors

Due to the ongoing miniaturization of devices quantum effects are no longer negligible in semiconductor modeling. Also temperature effects play a role for example when identifying hot spots in devices. QET models, which can be derived via moment method from the Wigner-BKG model, include both physical features. We analyze the stability of stationary states. Suitable numerical methods and computational results are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors

The asymptotic behavior of classical solutions of the bipolar hydrodynamical model for semiconductors is considered in the present paper. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equation. The global existence of classical solutions is proven, and the nonlinear diffusive phenomena is observed in large time in the sense that both densities of electron and hole tend to the same unique nonlinear diffusive wave.     

Nonlinear nonviscous hydrodynamical models for charge transport in the framework of extended thermodynamic methods

This paper develops a procedure, based on methods of extended thermodynamics, to design nonlinear hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. Models obtained in this way allow the study of the motion of electric charges in the presence of arbitrary external electric fields and may be useful when one wishes to study phenomena in a neighborhood of a stationary nonequilibrium process: indeed, the drift velocity of the charge gas with respect to the crystal lattice is not regarded as a small parameter.     

Theoretical foundations for tail electron hydrodynamical models in semiconductors

In this article, we present a theoretical foundation for tail electron hydrodynamical models (TEHM) in semiconductors.     

A hydrodynamical model for holes in silicon semiconductors: The case of non-parabolic warped bands

This paper can be considered as the natural prosecution of Mascali and Romano (2009) [5]. Here, we describe the motion of holes in silicon by also taking into account the non-parabolicity of the heavy and light bands. The model is still based on the moment method and the closure of the system of equations is obtained by using the maximum entropy principle. Comparisons are made with the results in [5], in the case of bulk silicon, in order to establish the importance of non-parabolicity.     

Global existence for the system of the macroscopic balance equations of charge transport in semiconductors

Global existence of a solution to the nonlinear balance equations of charge transport in semiconductors based on the maximum entropy principle [Contin. Mech. Thermodyn. 11 (1999) 307-325; Contin. Mech. Thermodyn. 12 (2000) 31-51] is proven for a typical 1D problem under certain restrictions on the doping profile and the initial data.     

A review of hydrodynamical models for semiconductors: Asymptotic behavior

We review recent results on the hydrodynamical model for semiconductors. The derivation of the mathematical model from the semi-classical Boltzmann equation in terms of the moment method is performed, and the mathematical analysis of the asymptotic behavior of both classical solutions and entropy weak solutions is given on spatially bounded domain or whole space.Dedicated to Constantine Dafermos on his 60^th birthday     

Stability of the equilibrium state of the equation system of a viscous barotropic gas in the model of atmosphere

Abstract We consider the system of equations of viscous gas motion whose pressure is related to the density by the law with 1<γ <2, in a domain defined by two levels of geopotential. Under the force due to geopotential and the Coriolis force, we prove the stability of the equilibrium state in a suitable Sobolev space. Keywords: Viscous barotropic gas, Equilibrium state, Coriolis force Mathematics Subject Classification (2000): 35Q35, 76N15     

A steady state potential flow model for semiconductors

Summary We present a three-dimensional steady state irrotational flow model for semiconductors which is based on the hydrodynamic equations. We prove existence and local uniqueness of smooth solutions under a smallness assumptions on the data. This assumption implies subsonic flow of electrons in the semiconductors device.     

Mathematical properties of a kinetic transport model for carriers and phonons in semiconductors

We present studies on the mathematical properties of a multigroup formulation of the Bloch–Boltzmann–Peierls equations. The considered model equations are based on a general carrier dispersion law and contain the full quantum statistics of both the carriers and the phonons. Moreover, the transport model allows the investigation of particle distributions with arbitrary anisotropy with respect to the main direction. We prove the boundedness of the solution according to the Pauli principle and study the conservational properties of the multigroup equations. In addition, the existence of a Lyapounov functional to the proposed model equations is proved and expressions for the equilibrium solution are given. Numerical results are presented for the stationary state distributions of a coupled system of electrons and longitudinal optical phonons in GaAs.     

Existence analysis for a simplified transient energy‐transport model for semiconductors

A simplified transient energy‐transport system for semiconductors subject to mixed Dirichlet–Neumann boundary conditions is analyzed. The model is formally derived from the non‐isothermal hydrodynamic equations in a particular vanishing momentum relaxation limit. It consists of a drift‐diffusion‐type equation for the electron density, involving temperature gradients, a nonlinear heat equation for the electron temperature, and the Poisson equation for the electric potential. The global‐in‐time existence of bounded weak solutions is proved. The proof is based on the Stampacchia truncation method and a careful use of the temperature equation. Under some regularity assumptions on the gradients of the variables, the uniqueness of solutions is shown. Finally, numerical simulations for a ballistic diode in one space dimension illustrate the behavior of the solutions. Copyright © 2012 John Wiley & Sons, Ltd.