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Author: Fuhrmann, Jürgen × End date: 2024 × Start date: 2020 × DDC: 510 × WGL Institute: WIAS ×

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Now showing 1 - 5 of 5
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    Entropy and convergence analysis for two finite volume schemes for a Nernst–Planck–Poisson system with ion volume constraints
    (Berlin ; Heidelberg : Springer, 2022) Gaudeul, Benoît; Fuhrmann, Jürgen
    In this paper, we consider a drift-diffusion system with cross-coupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the self-consistent electric field maintained by the ions and described by a Poisson equation. We design two finite volume schemes based on different formulations of the fluxes. We also provide a stability analysis of these schemes and an existence result for the corresponding discrete solutions. A convergence proof is proposed for non-degenerate solutions. Numerical experiments show the behavior of these schemes.
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    Entropy and convergence analysis for two finite volume schemes for a Nernst--Planck--Poisson system with ion volume constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Gaudeul, Benoît; Fuhrmann, Jürgen
    In this paper, we consider a drift-diffusion system with cross-coupling through the chemical potentials comprising a model for the motion of finite size ions in liquid electrolytes. The drift term is due to the self-consistent electric field maintained by the ions and described by a Poisson equation. We design two finite volume schemes based on different formulations of the fluxes. We also provide a stability analysis of these schemes and an existence result for the corresponding discrete solutions. A convergence proof is proposed for non-degenerate solutions. Numerical experiments show the behavior of these schemes.
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    Modelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Abdel, Dilara; Vágner, Petr; Fuhrmann, Jürgen; Farrell, Patricio
    From Maxwell--Stefan diffusion and general electrostatics, we derive a drift-diffusion model for charge transport in perovskite solar cells (PSCs) where any ion in the perovskite layer may flexibly be chosen to be mobile or immobile. Unlike other models in the literature, our model is based on quasi Fermi potentials instead of densities. This allows to easily include nonlinear diffusion (based on Fermi--Dirac, Gauss--Fermi or Blakemore statistics for example) as well as limit the ion depletion (via the Fermi--Dirac integral of order-1). The latter will be motivated by a grand-canonical formalism of ideal lattice gas. Furthermore, our model allows to use different statistics for different species. We discuss the thermodynamic equilibrium, electroneutrality as well as generation/recombination. Finally, we present numerical finite volume simulations to underline the importance of limiting ion depletion.
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    Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Abdel, Dilara; Farrell, Patricio; Fuhrmann, Jürgen
    The van Roosbroeck system models current flows in (non-)degenerate semiconductor devices. Focusing on the stationary model, we compare the excess chemical potential discretization scheme, a flux approximation which is based on a modification of the drift term in the current densities, with another state-of-the-art Scharfetter-Gummel scheme, namely the diffusion-enhanced scheme. Physically, the diffusion-enhanced scheme can be interpreted as a flux approximation which modifies the thermal voltage. As a reference solution we consider an implicitly defined integral flux, using Blakemore statistics. The integral flux refers to the exact solution of a local two point boundary value problem for the continuous current density and can be interpreted as a generalized Scharfetter-Gummel scheme. All numerical discretization schemes can be used within a Voronoi finite volume method to simulate charge transport in (non-)degenerate semiconductor devices. The investigation includes the analysis of Taylor expansions, a derivation of error estimates and a visualization of errors in local flux approximations to extend previous discussions. Additionally, drift-diffusion simulations of a p-i-n device are performed.
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    Generalized Poisson--Nernst--Planck-based physical model of O$_2$ I LSM I YSZ electrode
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Miloš, Vojtěch; Vágner, Petr; Budáč, Daniel; Carda, Michal; Paidar, Martin; Fuhrmann, Jürgen; Bouzek, Karel
    The paper presents a generalized Poisson-Nernst-Planck model of an yttria-stabilized zirconia electrolyte developed from first principles of nonequilibrium thermodynamics which allows for spatial resolution of the space charge layer. It takes into account limitations in oxide ion concentrations due to the limited availability of oxygen vacancies. The electrolyte model is coupled with a reaction kinetic model describing the triple phase boundary with electron conducting lanthanum strontium manganite and gaseous phase oxygen. By comparing the outcome of numerical simulations based on different formulations of the kinetic equations with results of EIS and CV measurements we attempt to discern the existence of separate surface lattice sites for oxygen adatoms and O2- from the assumption of shared ones. Furthermore, we discern mass-action kinetics models from exponential kinetics models.