The 3D transient semiconductor equations with gradient-dependent and interfacial recombination

TL;DR

This paper proves the well-posedness of a complex 3D semiconductor model with realistic conditions, including surface recombination and electric field dependencies, using advanced mathematical regularity theories.

Contribution

It extends the mathematical analysis of the van Roosbroeck system to more realistic and complex scenarios involving discontinuous data and interfacial effects.

Findings

Well-posedness of the 3D transient semiconductor equations established.

Inclusion of surface and interfacial recombination effects.

Application of maximal parabolic and elliptic regularity results.

Abstract

We establish the well-posedness of the transient van Roosbroeck system in three space dimensions under realistic assumptions on the data: non-smooth domains, discontinuous coefficient functions and mixed boundary conditions. Moreover, within this analysis, recombination terms may be concentrated on surfaces and interfaces and may not only depend on charge-carrier densities, but also on the electric field and currents. In particular, this includes Avalanche recombination. The proofs are based on recent abstract results on maximal parabolic and optimal elliptic regularity of divergence-form operators.