@article{7866,
abstract = {In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation.},
author = {Fellner, Klemens and Kniely, Michael},
issn = {22969039},
journal = {Journal of Elliptic and Parabolic Equations},
publisher = {Springer Nature},
title = {{Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model}},
doi = {10.1007/s41808-020-00068-8},
year = {2020},
}
@article{6762,
abstract = {We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level
of theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the doping profiles < system size.},
author = {Friesecke, Gero and Kniely, Michael},
issn = {15403467},
journal = {Multiscale Modeling and Simulation},
number = {3},
pages = {926--947},
publisher = {SIAM},
title = {{New optimal control problems in density functional theory motivated by photovoltaics}},
doi = {10.1137/18M1207272},
volume = {17},
year = {2019},
}