Filters

2020 - 20224

More filters

20224
Reset filters

Settings

Author: Liero, Matthias × Author: Nika, Grigor × End date: 2024 × Start date: 2020 × Has files: Yes × WGL Institute: WIAS ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    An effective bulk-surface thermistor model for large-area organic light-emitting diodes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Glitzky, Annegret; Liero, Matthias; Nika, Grigor
    The existence of a weak solution for an effective system of partial differential equations describing the electrothermal behavior of large-area organic light-emitting diodes (OLEDs) is proved. The effective system consists of the heat equation in the three-dimensional bulk glass substrate and two semi-linear equations for the current flow through the electrodes coupled to algebraic equations for the continuity of the electrical fluxes through the organic layers. The electrical problem is formulated on the (curvilinear) surface of the glass substrate where the OLED is mounted. The source terms in the heat equation are due to Joule heating and are hence concentrated on the part of the boundary where the current-flow equation is posed. The existence of weak solutions to the effective system is proved via Schauder's fixed-point theorem. Moreover, since the heat sources are a priori only in $L^1$, the concept of entropy solutions is used.
  • Thumbnail Image
    Item
    Dimension reduction of thermistor models for large-area organic light-emitting diodes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Glitzky, Annegret; Liero, Matthias; Nika, Grigor
    An effective system of partial differential equations describing the heat and current flow through a thin organic light-emitting diode (OLED) mounted on a glass substrate is rigorously derived from a recently introduced fully three-dimensional φ(x)-Laplace thermistor model. The OLED consists of several thin layers that scale differently with respect to the multiscale parameter ε > 0 which is the ratio between the total thickness and the lateral extent of the OLED. Starting point of the derivation is a rescaled formulation of the current-flow equation in the OLED for the driving potential and the heat equation in OLED and glass substrate with Joule heat term concentrated in the OLED. Assuming physically motivated scalings in the electrical flux functions, uniform a priori bounds are derived for the solutions of the three-dimensional system which facilitates the extraction of converging subsequences with limits that are identified as solutions of a dimension reduced system. In the latter, the effective current-flow equation is given by two semilinear equations in the two-dimensional cross-sections of the electrodes and algebraic equations for the continuity of the electrical fluxes through the organic layers. The effective heat equation is formulated only in the glass substrate with Joule heat term on the part of the boundary where the OLED is mounted.
  • Thumbnail Image
    Item
    A coarse-grained electrothermal model for organic semiconductor devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Glitzky, Annegret; Liero, Matthias; Nika, Grigor
    We derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion based electrothermal models with thermistor type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss--Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.
  • Thumbnail Image
    Item
    A coarse‐grained electrothermal model for organic semiconductor devices
    (Chichester, West Sussex : Wiley, 2022) Glitzky, Annegret; Liero, Matthias; Nika, Grigor
    We derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion- based electrothermal models with thermistor-type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss–Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.