Stationary energy models for semiconductor devices with incompletely ionized impurities

Abstract

The paper deals with two‐dimensional stationary energy models for semiconductor devices, which contain incompletely ionized impurities. We reduce the problem to a strongly coupled nonlinear system of four equations, which is elliptic in nondegenerated states. Heterostructures as well as mixed boundary conditions have to be taken into account. For boundary data which are compatible with thermodynamic equilibrium there exists a thermodynamic equilibrium. Using regularity results for systems of strongly coupled linear elliptic differential equations with mixed boundary conditions and nonsmooth data and applying the Implicit Function Theorem we prove that in a suitable neighbourhood of such a thermodynamic equilibrium there exists a unique stationary solution, too.

Resolvent estimates in W−1,p related to strongly coupled‐linear parabolic systems with coupled nonsmooth capacities

“…Since linearizations of such problems in thermodynamic equilibria lead to problems of the form (1), the implicit function theorem could supply a local existence and uniqueness result for such problems for data near data compatible to thermodynamic equilibrium. Such techniques have been successfully applied to strongly coupled elliptic problems with coefficients depending on the state in [11,12].…”

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.…”

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

“…Moreover, the different domains of definition of the relevant model equations are taken into account. For the case that Ω and Ω 0 coincide we have investigated an energy model containing incompletely ionized impurities in [9] and a multi species version of the above energy model in [8].…”