The 3D transient semiconductor equations with gradient-dependent and interfacial recombination
- Disser, Karoline
- Rehberg, Joachim
2010 Mathematics Subject Classification
- 35K57 35K55 78A35 35R05 35K45
- Van Roosbroeck's system, semiconductor device, Avalanche recombination, surface recombination, nonlinear parabolic system, heterogeneous material, discontinuous coefficients and data, mixed boundary conditions
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.
- Math. Models Methods Appl. Sci., 29 (2019), pp. 1819--1851, DOI 10.1142/S0218202519500350 .