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Author: Liero, Matthias × Author: Nika, Grigor × End date: 2022 × Start date: 2020 × End date: 2019 × Start date: 2010 × Has files: Yes × Version: publishedVersion × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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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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    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.
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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.