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- ItemStationary solutions to an energy model for semiconductor devices where the equations are defined on different domains(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Glitzky, Annegret; Hünlich, RolfWe discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain $Omega_0$ of the domain of definition $Omega$ of the energy balance equation and of the Poisson equation. Here $Omega_0$ corresponds to the region of semiconducting material, $OmegasetminusOmega_0$ represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two-dimensional stationary energy model. For this purpose we derive a $W^1,p$-regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem.
- ItemDiscrete Sobolev-Poincare inequalities for Voronoi finite volume approximations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Glitzky, Annegret; Griepentrog, Jens AndréWe prove a discrete Sobolev-Poincare inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev's integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove a discrete Poincare inequality for space dimensions greater or equal to two.
- ItemA coarse-grained electrothermal model for organic semiconductor devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Glitzky, Annegret; Liero, Matthias; Nika, GrigorWe 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.
- ItemAn 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, GrigorThe 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.
- ItemAnalysis 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, GrigorWe 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.
- ItemDrift-diffusion modeling, analysis and simulation of organic semiconductor devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Doan, Duy-Hai; Glitzky, Annegret; Liero, MatthiasWe discuss drift-diffusion models for charge-carrier transport in organic semiconductor devices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The former leads to so-called Gauss-Fermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlinear dependence on temperature, density of carriers, and electric field strength. We present the state-of-the-art modeling of the transport processes and provide a first existence result for the stationary drift-diffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauders fixed-point theorem. Finally, we discuss the numerical discretization of the model using finite-volume methods and a generalized Scharfetter-Gummel scheme for the Gauss-Fermi statistics.
- ItemDrift-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, MatthiasWe 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.
- ItemEnergy estimates for electro-reaction-diffusion systems with partly fast kinetics(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Glitzky, AnnegretWe start from a basic model for the transport of charged species in heterostructures containing the mechanisms diffusion, drift and reactions in the domain and at its boundary. Considering limit cases of partly fast kinetics we derive reduced models. This reduction can be interpreted as some kind of projection scheme for the weak formulation of the basic electro--reaction--diffusion system. We verify assertions concerning invariants and steady states and prove the monotone and exponential decay of the free energy along solutions to the reduced problem and to its fully implicit discrete-time version by means of the results of the basic problem. Moreover we make a comparison of prolongated quantities with the solutions to the basic model.
- ItemConvergence of an implicit Voronoi finite volume method for reaction-diffusion problems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Fiebach, André; Glitzky, Annegret; Linke, AlexanderWe investigate the convergence of an implicit Voronoi finite volume method for reaction- diffusion problems including nonlinear diffusion in two space dimensions. The model allows to handle heterogeneous materials and uses the chemical potentials of the involved species as primary variables. The numerical scheme uses boundary conforming Delaunay meshes and preserves positivity and the dissipative property of the continuous system. Starting from a result on the global stability of the scheme (uniform, mesh-independent global upper and lower bounds), we prove strong convergence of the chemical activities and their gradients to a weak solution of the continuous problem. In order to illustrate the preservation of qualitative properties by the numerical scheme, we present a long-term simulation of the Michaelis-Menten-Henri system. Especially, we investigate the decay properties of the relative free energy and the evolution of the dissipation rate over several magnitudes of time, and obtain experimental orders of convergence for these quantities.
- ItemFeel the heat: Nonlinear electrothermal feedback in organic LEDs(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Fischer, Axel; Koprucki, Thomas; Gärtner, Klaus; Tietze, Max L.; Brückner, Jacqueline; Lüssem, Björn; Leo, Karl; Glitzky, Annegret; Scholz, ReinhardFor lighting applications, Organic light-emitting diodes (OLED) need much higher brightness than for displays, leading to self-heating. Due to the temperature-activated transport in organic semiconductors, this can result in brightness inhomogeneities and catastrophic failure. Here, we show that due to the strong electrothermal feedback of OLEDs, the common spatial current and voltage distribution is completely changed, requiring advanced device modeling and operation concepts. Our study clearly demonstrates the effect of negative differential resistance (NDR) in OLEDs induced by self-heating. As a consequence, for increasing voltage, regions with declining voltages are propagating through the device, and even more interestingly, a part of these regions show even decreasing currents, leading to strong local variation in luminance. The expected breakthrough of OLED lighting technology will require an improved price performance ratio, and the realization of modules with very high brightness but untainted appearance is considered to be an essential step into this direction. Thus, a deeper understanding of the control of electrothermal feedback will help to make OLEDs in lighting more competitive.