Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains

Abstract

We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain Ω0 of the domain of definition Ω of the energy balance equation and of the Poisson equation. Here Ω0 corresponds to the region of semiconducting material, Ω \ Ω0 represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two‐dimensional stationary energy model. For this purpose we derive a W1,p ‐regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Study of a Finite Volume Scheme for the Drift-Diffusion System. Asymptotic Behavior in the Quasi-Neutral Limit

“…The linear system (30) can be written under the matricial form A N N T = S n N where the matrix A N is defined by:…”

“…Generally, it provides the convergence in relative entropy of the evolutive solution towards an equilibrium state. This method has been widely applied to many different systems: see [1] and the references therein, but also [39,22,16,30,29]... However, the entropy method also permits to get new a priori estimates on systems of partial differential equations via a bound on the entropy production, see [37,25,26] for instance.…”

Existence of Bounded Steady State Solutions to Spin-Polarized Drift-Diffusion Systems

“…From Theorem 2.1 we obtain Remark 2.4 In [8,9] we investigated stationary energy models for semiconductor devices which correspond to strongly coupled elliptic systems. To obtain in two space dimensions a local existence and uniqueness result for data nearly compatible with thermodynamic equilibrium we used there regularity and surjectivity results in W 1,p (Ω), p > 2 and applied the implicit function theorem in that scale of spaces.…”

Energy transport in semiconductor devices

“…Stationary energy-transport equations which are defined on different domains have been examined in [52]. Near-equilibrium solutions to the time-dependent equations have been found in [36,38].…”