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Author: Liero, Matthias × End date: 2022 × Start date: 2020 × End date: 2019 × Start date: 2010 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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Now showing 1 - 5 of 5
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    Effective diffusion in thin structures via generalized gradient systems and EDP-convergence
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Frenzel, Thomas; Liero, Matthias
    The notion of Energy-Dissipation-Principle convergence (EDP-convergence) is used to derive effective evolution equations for gradient systems describing diffusion in a structure consisting of several thin layers in the limit of vanishing layer thickness. The thicknesses of the sublayers tend to zero with different rates and the diffusion coefficients scale suitably. The Fokker--Planck equation can be formulated as gradient-flow equation with respect to the logarithmic relative entropy of the system and a quadratic Wasserstein-type gradient structure. The EDP-convergence of the gradient system is shown by proving suitable asymptotic lower limits of the entropy and the total dissipation functional. The crucial point is that the limiting evolution is again described by a gradient system, however, now the dissipation potential is not longer quadratic but is given in terms of the hyperbolic cosine. The latter describes jump processes across the thin layers and is related to the Marcelin--de Donder kinetics.
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    An existence result for a class of electrothermal drift-diffusion models with Gauss--Fermi statistics for organic semiconductors
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Glitzky, Annegret; Liero, Matthias; Nika, Grigor
    This work is concerned with the analysis of a drift-diffusion model for the electrothermal behavior of organic semiconductor devices. A "generalized Van Roosbroeck'' system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like Gauss--Fermi statistics and mobilities functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder's fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that self-heating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal drift-diffusion model for organic semiconductors on a sound analytical basis.
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    Analysis of a hybrid model for the electrothermal behavior of semiconductor heterostructures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Glitzky, Annegret; Liero, Matthias; Nika, Grigor
    We prove existence of a weak solution for a hybrid model for the electro-thermal behavior of semiconductor heterostructures. This hybrid model combines an electro-thermal model based on drift-diffusion with thermistor type models in different subregions of the semiconductor heterostructure. The proof uses a regularization method and Schauder's fixed point theorem. For boundary data compatible with thermodynamic equilibrium we verify, additionally, uniqueness. Moreover, we derive bounds and higher integrability properties for the electrostatic potential and the quasi Fermi potentials as well as the temperature.
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    Drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Doan, Duy Hai; Fischer, Axel; Fuhrmann, Jürgen; Glitzky, Annegret; Liero, Matthias
    We present an electrothermal drift-diffusion model for organic semiconductor devices with Gauss-Fermi statistics and positive temperature feedback for the charge carrier mobilities. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and discretize the system by a finite volume based generalized Scharfetter-Gummel scheme. Using path-following techniques we demonstrate that the model exhibits S-shaped current-voltage curves with regions of negative differential resistance, which were only recently observed experimentally.
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    Unipolar drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Fuhrmann, Jürgen; Doan, Duy Hai; Glitzky, Annegret; Liero, Matthias; Nika, Grigor
    We discretize a unipolar electrothermal drift-diffusion model for organic semiconductor devices with Gauss--Fermi statistics and charge carrier mobilities having positive temperature feedback. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and use a finite volume based generalized Scharfetter-Gummel scheme. Applying path-following techniques we demonstrate that the model exhibits S-shaped current-voltage curves with regions of negative differential resistance, only recently observed experimentally.